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287 results on '"Walker, Alexander P."'

1. Self-Correlations of Hurwitz Class Numbers

Author

Walker, Alexander

Subjects
Mathematics - Number Theory, 11Mxx
Abstract

The asymptotic study of class numbers of binary quadratic forms is a foundational problem in arithmetic statistics. Here, we investigate finer statistics of class numbers by studying their self-correlations under additive shifts. Specifically, we produce uniform asymptotics for the shifted convolution sum $\sum_{n < X} H(n) H(n+\ell)$ for fixed $\ell \in \mathbb{Z}$, in which $H(n)$ denotes the Hurwitz class number., Comment: 41 pages, 0 figures

Published
2024

2. Counting Divisors in the Outputs of a Binary Quadratic Form

Author

Kuan, Chan Ieong, Lowry-Duda, David, Walker, Alexander, and Huang, Tinghao

Subjects
Mathematics - Number Theory, 11F30, 11N37, 11F72
Abstract

For a fixed natural number $h$, we prove meromorphic continuation of the two-variable Dirichlet series $\sum_m r_2(m) \sigma_w(m + h) (m + h)^{-s + w}$ to $\mathbb{C}^2$ and use this to obtain asymptotics for $\sum_{m^2 + n^2 \leq X} \sigma_w(m^2 + n^2 + h)$. We approach this continuation through spectral theory. Our results are comparable to earlier work of Bykovskii, who used different methods to study the sums $\sum_{n^2 \leq X} \sigma_w(n^2 + h)$., Comment: 41 pages, including an appendix by Kuan and Huang

Published
2023

4. Sums of Cusp Form Coefficients Along Quadratic Sequences

Author

Kuan, Chan Ieong, Lowry-Duda, David, Walker, Alexander, and Steiner, Raphael S.

Subjects
Mathematics - Number Theory
Abstract

Let $f(z) = \sum A(n) n^{(k-1)/2} e(nz)$ be a cusp form of weight $k \geq 3$ on $\Gamma_0(N)$ with character $\chi$. By studying a certain shifted convolution sum, we prove that $\sum_{n \leq X} A(n^2+h) = c_{f,h} X + O_{f,h,\epsilon}(X^{\frac{3}{4}+\epsilon})$ for $\epsilon>0$, which improves a result of Blomer from 2008 with error $X^{\frac{6}{7}+\epsilon}$. This includes an appendix due to Raphael S. Steiner, proving stronger bounds for certain spectral averages., Comment: 22 pages, with a 14 page appendix from Raphael S. Steiner. This version corrects a mistake in the previous, where lifts of holomorphic modular forms to Maass forms were omitted; and it has an updated abstract

Published
2023

5. Integer Sets of Large Harmonic Sum Which Avoid Long Arithmetic Progressions

Author

Walker, Alexander

Subjects
Mathematics - Number Theory, Mathematics - Combinatorics, 11Y55, 11Y60
Abstract

We give conditions under which certain digit-restricted integer sets avoid $k$-term arithmetic progressions. These sets are reasonably efficient to compute and therefore enable large-scale search. We identify a set with no arithmetic progression of four terms and with harmonic sum $4.43975$, which improves an earlier "greedy" construction., Comment: 9 pages, 0 figures

Published
2022

7. Social and moral psychology of COVID-19 across 69 countries

Author

Azevedo, Flavio, Pavlović, Tomislav, Rêgo, Gabriel G., Ay, F. Ceren, Gjoneska, Biljana, Etienne, Tom W., Ross, Robert M., Schönegger, Philipp, Riaño-Moreno, Julián C., Cichocka, Aleksandra, Capraro, Valerio, Cian, Luca, Longoni, Chiara, Chan, Ho Fai, Van Bavel, Jay J., Sjåstad, Hallgeir, Nezlek, John B., Alfano, Mark, Gelfand, Michele J., Birtel, Michèle D., Cislak, Aleksandra, Lockwood, Patricia L., Abts, Koen, Agadullina, Elena, Aruta, John Jamir Benzon, Besharati, Sahba Nomvula, Bor, Alexander, Choma, Becky L., Crabtree, Charles David, Cunningham, William A., De, Koustav, Ejaz, Waqas, Elbaek, Christian T., Findor, Andrej, Flichtentrei, Daniel, Franc, Renata, Gruber, June, Gualda, Estrella, Horiuchi, Yusaku, Huynh, Toan Luu Duc, Ibanez, Agustin, Imran, Mostak Ahamed, Israelashvili, Jacob, Jasko, Katarzyna, Kantorowicz, Jaroslaw, Kantorowicz-Reznichenko, Elena, Krouwel, André, Laakasuo, Michael, Lamm, Claus, Leygue, Caroline, Lin, Ming-Jen, Mansoor, Mohammad Sabbir, Marie, Antoine, Mayiwar, Lewend, Mazepus, Honorata, McHugh, Cillian, Minda, John Paul, Mitkidis, Panagiotis, Olsson, Andreas, Otterbring, Tobias, Packer, Dominic J., Perry, Anat, Petersen, Michael Bang, Puthillam, Arathy, Rothmund, Tobias, Santamaría-García, Hernando, Schmid, Petra C., Stoyanov, Drozdstoy, Tewari, Shruti, Todosijević, Bojan, Tsakiris, Manos, Tung, Hans H., Umbres, Radu G., Vanags, Edmunds, Vlasceanu, Madalina, Vonasch, Andrew, Yucel, Meltem, Zhang, Yucheng, Abad, Mohcine, Adler, Eli, Akrawi, Narin, Mdarhri, Hamza Alaoui, Amara, Hanane, Amodio, David M., Antazo, Benedict G., Apps, Matthew, Ba, Mouhamadou Hady, Barbosa, Sergio, Bastian, Brock, Berg, Anton, Bernal-Zárate, Maria P., Bernstein, Michael, Białek, Michał, Bilancini, Ennio, Bogatyreva, Natalia, Boncinelli, Leonardo, Booth, Jonathan E., Borau, Sylvie, Buchel, Ondrej, Cameron, C. Daryl, Carvalho, Chrissie F., Celadin, Tatiana, Cerami, Chiara, Chalise, Hom Nath, Cheng, Xiaojun, Cockcroft, Kate, Conway, Jane, Córdoba-Delgado, Mateo Andres, Crespi, Chiara, Crouzevialle, Marie, Cutler, Jo, Cypryańska, Marzena, Dabrowska, Justyna, Daniels, Michael A., Davis, Victoria H., Dayley, Pamala N., Delouvée, Sylvain, Denkovski, Ognjan, Dezecache, Guillaume, Dhaliwal, Nathan A., Diato, Alelie B., Di Paolo, Roberto, Drosinou, Marianna, Dulleck, Uwe, Ekmanis, Jānis, Ertan, Arhan S., Farhana, Hapsa Hossain, Farkhari, Fahima, Farmer, Harry, Fenwick, Ali, Fidanovski, Kristijan, Flew, Terry, Fraser, Shona, Frempong, Raymond Boadi, Fugelsang, Jonathan A., Gale, Jessica, Garcia-Navarro, E. Begoña, Garladinne, Prasad, Ghajjou, Oussama, Gkinopoulos, Theofilos, Gray, Kurt, Griffin, Siobhán M., Gronfeldt, Bjarki, Gümren, Mert, Gurung, Ranju Lama, Halperin, Eran, Harris, Elizabeth, Herzon, Volo, Hruška, Matej, Huang, Guanxiong, Hudecek, Matthias F. C., Isler, Ozan, Jangard, Simon, Jorgensen, Frederik J., Kachanoff, Frank, Kahn, John, Dangol, Apsara Katuwal, Keudel, Oleksandra, Koppel, Lina, Koverola, Mika, Kubin, Emily, Kunnari, Anton, Kutiyski, Yordan, Laguna, Oscar Moreda, Leota, Josh, Lermer, Eva, Levy, Jonathan, Levy, Neil, Li, Chunyun, Long, Elizabeth U., Maglić, Marina, McCashin, Darragh, Metcalf, Alexander L., Mikloušić, Igor, El Mimouni, Soulaimane, Miura, Asako, Molina-Paredes, Juliana, Monroy-Fonseca, César, Morales-Marente, Elena, Moreau, David, Muda, Rafał, Myer, Annalisa, Nash, Kyle, Nesh-Nash, Tarik, Nitschke, Jonas P., Nurse, Matthew S., Ohtsubo, Yohsuke, de Mello, Victoria Oldemburgo, O’Madagain, Cathal, Onderco, Michal, Palacios-Galvez, M. Soledad, Palomöki, Jussi, Pan, Yafeng, Papp, Zsófia, Pärnamets, Philip, Paruzel-Czachura, Mariola, Pavlović, Zoran, Payán-Gómez, César, Perander, Silva, Pitman, Michael Mark, Prasad, Rajib, Pyrkosz-Pacyna, Joanna, Rathje, Steve, Raza, Ali, Rhee, Kasey, Robertson, Claire E., Rodríguez-Pascual, Iván, Saikkonen, Teemu, Salvador-Ginez, Octavio, Santi, Gaia C., Santiago-Tovar, Natalia, Savage, David, Scheffer, Julian A., Schultner, David T., Schutte, Enid M., Scott, Andy, Sharma, Madhavi, Sharma, Pujan, Skali, Ahmed, Stadelmann, David, Stafford, Clara Alexandra, Stanojević, Dragan, Stefaniak, Anna, Sternisko, Anni, Stoica, Augustin, Stoyanova, Kristina K., Strickland, Brent, Sundvall, Jukka, Thomas, Jeffrey P., Tinghög, Gustav, Torgler, Benno, Traast, Iris J., Tucciarelli, Raffaele, Tyrala, Michael, Ungson, Nick D., Uysal, Mete S., Van Lange, Paul A. M., van Prooijen, Jan-Willem, van Rooy, Dirk, Västfjäll, Daniel, Verkoeijen, Peter, Vieira, Joana B., von Sikorski, Christian, Walker, Alexander Cameron, Watermeyer, Jennifer, Wetter, Erik, Whillans, Ashley, White, Katherine, Habib, Rishad, Willardt, Robin, Wohl, Michael J. A., Wójcik, Adrian Dominik, Wu, Kaidi, Yamada, Yuki, Yilmaz, Onurcan, Yogeeswaran, Kumar, Ziemer, Carolin-Theresa, Zwaan, Rolf A., Boggio, Paulo S., and Sampaio, Waldir M.

Published
2023
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8. Controlling the narrative: Euphemistic language affects judgments of actions while avoiding perceptions of dishonesty

Author

Walker, Alexander C., Turpin, Martin, Meyers, Ethan, Stolz, Jennifer, Fugelsang, Jonathan, and Koehler, Derek

Subjects
Psychology, Decision making, Language and thought, Social cognition, Survey
Abstract

The present work examined the extent to which evaluations of actions could be biased by the strategic use of euphemistic (agreeable) and dysphemistic (disagreeable) terms. Across multiple studies, we demonstrate that evaluations of actions are made more favorable by replacing a disagreeable term (e.g., torture) with a semantically related agreeable term (e.g., enhanced interrogation) in an act’s description. Notably, the influence of these terms was reduced (but not eliminated) when actions were described in a less ambiguous (i.e., more detailed) manner. Despite their influence, participants judged both agreeable and disagreeable action descriptions as largely truthful and distinct from lies, and judged agents using such descriptions as more trustworthy and moral than liars. Overall, the present findings suggest that a strategic speaker can, through the careful use of language, sway the opinions of others while avoiding many of the reputational costs associated with less subtle forms of linguistic manipulation (e.g., lying).

Published
2022

11. Arithmetic Progressions of Squares and Multiple Dirichlet Series

Author

Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander

Subjects
Mathematics - Number Theory, 11N37 (Primary), 11F30 (Secondary)
Abstract

We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic continuation to $\mathbb{C}^2$ and use Tauberian methods to obtain counts for arithmetic progressions of squares and rational points on $x^2+y^2=2$., Comment: 32 pages, now revised with referee comments

Published
2020

12. Triple Correlation Sums of Coefficients of Cusp Forms

Author

Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander

Subjects
Mathematics - Number Theory, 11F11, 11M32
Abstract

We produce nontrivial asymptotic estimates for shifted sums of the form $\sum a(h)b(m)c(2m-h)$, in which $a(n),b(n),c(n)$ are un-normalized Fourier coefficients of holomorphic cusp forms. These results are unconditional, but we demonstrate how to strengthen them under the Riemann Hypothesis. As an application, we show that there are infinitely many three term arithmetic progressions $n-h, n, n+h$ such that $a(n-h)a(n)a(n+h) \neq 0$., Comment: 17 pages (now with consistent author naming)

Published
2019

14. Arithmetic Progressions with Restricted Digits

Author

Walker, Aled and Walker, Alexander

Subjects
Mathematics - Number Theory, Mathematics - Combinatorics
Abstract

For an integer $b \geqslant 2$ and a set $S\subset \{0,\cdots,b-1\}$, we define the Kempner set $\mathcal{K}(S,b)$ to be the set of all non-negative integers whose base-$b$ digital expansions contain only digits from $S$. These well-studied sparse sets provide a rich setting for additive number theory, and in this paper we study various questions relating to the appearance of arithmetic progressions in these sets. In particular, for all $b$ we determine exactly the maximal length of an arithmetic progression that omits a base-$b$ digit., Comment: 11 pages, submitted to American Mathematical Monthly

Published
2018

15. National identity predicts public health support during a global pandemic

Author

Van Bavel, Jay J., Cichocka, Aleksandra, Capraro, Valerio, Sjåstad, Hallgeir, Nezlek, John B., Pavlović, Tomislav, Alfano, Mark, Gelfand, Michele J., Azevedo, Flavio, Birtel, Michèle D., Cislak, Aleksandra, Lockwood, Patricia L., Ross, Robert Malcolm, Abts, Koen, Agadullina, Elena, Aruta, John Jamir Benzon, Besharati, Sahba Nomvula, Bor, Alexander, Choma, Becky L., Crabtree, Charles David, Cunningham, William A., De, Koustav, Ejaz, Waqas, Elbaek, Christian T., Findor, Andrej, Flichtentrei, Daniel, Franc, Renata, Gjoneska, Biljana, Gruber, June, Gualda, Estrella, Horiuchi, Yusaku, Huynh, Toan Luu Duc, Ibanez, Augustin, Imran, Mostak Ahamed, Israelashvili, Jacob, Jasko, Katarzyna, Kantorowicz, Jaroslaw, Kantorowicz-Reznichenko, Elena, Krouwel, André, Laakasuo, Michael, Lamm, Claus, Leygue, Caroline, Lin, Ming-Jen, Mansoor, Mohammad Sabbir, Marie, Antoine, Mayiwar, Lewend, Mazepus, Honorata, McHugh, Cillian, Minda, John Paul, Mitkidis, Panagiotis, Olsson, Andreas, Otterbring, Tobias, Packer, Dominic J., Perry, Anat, Petersen, Michael Bang, Puthillam, Arathy, Riaño-Moreno, Julián C., Rothmund, Tobias, Santamaría-García, Hernando, Schmid, Petra C., Stoyanov, Drozdstoy, Tewari, Shruti, Todosijević, Bojan, Tsakiris, Manos, Tung, Hans H., Umbreș, Radu G., Vanags, Edmunds, Vlasceanu, Madalina, Vonasch, Andrew, Yucel, Meltem, Zhang, Yucheng, Abad, Mohcine, Adler, Eli, Akrawi, Narin, Mdarhri, Hamza Alaoui, Amara, Hanane, Amodio, David M., Antazo, Benedict G., Apps, Matthew, Ay, F. Ceren, Ba, Mouhamadou Hady, Barbosa, Sergio, Bastian, Brock, Berg, Anton, Bernal-Zárate, Maria P., Bernstein, Michael, Białek, Michał, Bilancini, Ennio, Bogatyreva, Natalia, Boncinelli, Leonardo, Booth, Jonathan E., Borau, Sylvie, Buchel, Ondrej, Cameron, C. Daryl, Carvalho, Chrissie F., Celadin, Tatiana, Cerami, Chiara, Chalise, Hom Nath, Cheng, Xiaojun, Cian, Luca, Cockcroft, Kate, Conway, Jane, Córdoba-Delgado, Mateo Andres, Crespi, Chiara, Crouzevialle, Marie, Cutler, Jo, Cypryańska, Marzena, Dabrowska, Justyna, Daniels, Michael A., Davis, Victoria H., Dayley, Pamala N., Delouvee, Sylvain, Denkovski, Ognjan, Dezecache, Guillaume, Dhaliwal, Nathan A., Diato, Alelie B., Di Paolo, Roberto, Drosinou, Marianna, Dulleck, Uwe, Ekmanis, Jānis, Ertan, Arhan S., Etienne, Tom W., Farhana, Hapsa Hossain, Farkhari, Fahima, Farmer, Harry, Fenwick, Ali, Fidanovski, Kristijan, Flew, Terry, Fraser, Shona, Frempong, Raymond Boadi, Fugelsang, Jonathan A., Gale, Jessica, Garcia-Navarro, E. Begoña, Garladinne, Prasad, Ghajjou, Oussama, Gkinopoulos, Theofilos, Gray, Kurt, Griffin, Siobhán M., Gronfeldt, Bjarki, Gümren, Mert, Gurung, Ranju Lama, Halperin, Eran, Harris, Elizabeth, Herzon, Volo, Hruška, Matej, Huang, Guanxiong, Hudecek, Matthias F. C., Isler, Ozan, Jangard, Simon, Jørgensen, Frederik J., Kachanoff, Frank, Kahn, John, Dangol, Apsara Katuwal, Keudel, Oleksandra, Koppel, Lina, Koverola, Mika, Kubin, Emily, Kunnari, Anton, Kutiyski, Yordan, Laguna, Oscar, Leota, Josh, Lermer, Eva, Levy, Jonathan, Levy, Neil, Li, Chunyun, Long, Elizabeth U., Longoni, Chiara, Maglić, Marina, McCashin, Darragh, Metcalf, Alexander L., Mikloušić, Igor, El Mimouni, Soulaimane, Miura, Asako, Molina-Paredes, Juliana, Monroy-Fonseca, César, Morales-Marente, Elena, Moreau, David, Muda, Rafał, Myer, Annalisa, Nash, Kyle, Nesh-Nash, Tarik, Nitschke, Jonas P., Nurse, Matthew S., Ohtsubo, Yohsuke, Oldemburgo de Mello, Victoria, O’Madagain, Cathal, Onderco, Michal, Palacios-Galvez, M. Soledad, Palomäki, Jussi, Pan, Yafeng, Papp, Zsófia, Pärnamets, Philip, Paruzel-Czachura, Mariola, Pavlović, Zoran, Payán-Gómez, César, Perander, Silva, Pitman, Michael Mark, Prasad, Rajib, Pyrkosz-Pacyna, Joanna, Rathje, Steve, Raza, Ali, Rêgo, Gabriel G., Rhee, Kasey, Robertson, Claire E., Rodríguez-Pascual, Iván, Saikkonen, Teemu, Salvador-Ginez, Octavio, Sampaio, Waldir M., Santi, Gaia C., Santiago-Tovar, Natalia, Savage, David, Scheffer, Julian A., Schönegger, Philipp, Schultner, David T., Schutte, Enid M., Scott, Andy, Sharma, Madhavi, Sharma, Pujan, Skali, Ahmed, Stadelmann, David, Stafford, Clara Alexandra, Stanojević, Dragan, Stefaniak, Anna, Sternisko, Anni, Stoica, Augustin, Stoyanova, Kristina K., Strickland, Brent, Sundvall, Jukka, Thomas, Jeffrey P., Tinghög, Gustav, Torgler, Benno, Traast, Iris J., Tucciarelli, Raffaele, Tyrala, Michael, Ungson, Nick D., Uysal, Mete S., Van Lange, Paul A. M., van Prooijen, Jan-Willem, van Rooy, Dirk, Västfjäll, Daniel, Verkoeijen, Peter, Vieira, Joana B., von Sikorski, Christian, Walker, Alexander Cameron, Watermeyer, Jennifer, Wetter, Erik, Whillans, Ashley, Willardt, Robin, Wohl, Michael J. A., Wójcik, Adrian Dominik, Wu, Kaidi, Yamada, Yuki, Yilmaz, Onurcan, Yogeeswaran, Kumar, Ziemer, Carolin-Theresa, Zwaan, Rolf A., and Boggio, Paulo S.

Published
2022
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16. Author Correction: National identity predicts public health support during a global pandemic

Author

Van Bavel, Jay J., Cichocka, Aleksandra, Capraro, Valerio, Sjåstad, Hallgeir, Nezlek, John B., Pavlović, Tomislav, Alfano, Mark, Gelfand, Michele J., Azevedo, Flavio, Birtel, Michèle D., Cislak, Aleksandra, Lockwood, Patricia L., Ross, Robert Malcolm, Abts, Koen, Agadullina, Elena, Aruta, John Jamir Benzon, Besharati, Sahba Nomvula, Bor, Alexander, Choma, Becky L., Crabtree, Charles David, Cunningham, William A., De, Koustav, Ejaz, Waqas, Elbaek, Christian T., Findor, Andrej, Flichtentrei, Daniel, Franc, Renata, Gjoneska, Biljana, Gruber, June, Gualda, Estrella, Horiuchi, Yusaku, Huynh, Toan Luu Duc, Ibanez, Agustin, Imran, Mostak Ahamed, Israelashvili, Jacob, Jasko, Katarzyna, Kantorowicz, Jaroslaw, Kantorowicz-Reznichenko, Elena, Krouwel, André, Laakasuo, Michael, Lamm, Claus, Leygue, Caroline, Lin, Ming-Jen, Mansoor, Mohammad Sabbir, Marie, Antoine, Mayiwar, Lewend, Mazepus, Honorata, McHugh, Cillian, Minda, John Paul, Mitkidis, Panagiotis, Olsson, Andreas, Otterbring, Tobias, Packer, Dominic J., Perry, Anat, Petersen, Michael Bang, Puthillam, Arathy, Riaño-Moreno, Julián C., Rothmund, Tobias, Santamaría-García, Hernando, Schmid, Petra C., Stoyanov, Drozdstoy, Tewari, Shruti, Todosijević, Bojan, Tsakiris, Manos, Tung, Hans H., Umbreș, Radu G., Vanags, Edmunds, Vlasceanu, Madalina, Vonasch, Andrew, Yucel, Meltem, Zhang, Yucheng, Abad, Mohcine, Adler, Eli, Akrawi, Narin, Mdarhri, Hamza Alaoui, Amara, Hanane, Amodio, David M., Antazo, Benedict G., Apps, Matthew, Ay, F. Ceren, Ba, Mouhamadou Hady, Barbosa, Sergio, Bastian, Brock, Berg, Anton, Bernal-Zárate, Maria P., Bernstein, Michael, Białek, Michał, Bilancini, Ennio, Bogatyreva, Natalia, Boncinelli, Leonardo, Booth, Jonathan E., Borau, Sylvie, Buchel, Ondrej, Cameron, C. Daryl, Carvalho, Chrissie F., Celadin, Tatiana, Cerami, Chiara, Chalise, Hom Nath, Cheng, Xiaojun, Cian, Luca, Cockcroft, Kate, Conway, Jane, Córdoba-Delgado, Mateo Andres, Crespi, Chiara, Crouzevialle, Marie, Cutler, Jo, Cypryańska, Marzena, Dabrowska, Justyna, Daniels, Michael A., Davis, Victoria H., Dayley, Pamala N., Delouvee, Sylvain, Denkovski, Ognjan, Dezecache, Guillaume, Dhaliwal, Nathan A., Diato, Alelie B., Di Paolo, Roberto, Drosinou, Marianna, Dulleck, Uwe, Ekmanis, Jānis, Ertan, Arhan S., Etienne, Tom W., Farhana, Hapsa Hossain, Farkhari, Fahima, Farmer, Harry, Fenwick, Ali, Fidanovski, Kristijan, Flew, Terry, Fraser, Shona, Frempong, Raymond Boadi, Fugelsang, Jonathan A., Gale, Jessica, Garcia-Navarro, E. Begoña, Garladinne, Prasad, Ghajjou, Oussama, Gkinopoulos, Theofilos, Gray, Kurt, Griffin, Siobhán M., Gronfeldt, Bjarki, Gümren, Mert, Gurung, Ranju Lama, Halperin, Eran, Harris, Elizabeth, Herzon, Volo, Hruška, Matej, Huang, Guanxiong, Hudecek, Matthias F. C., Isler, Ozan, Jangard, Simon, Jørgensen, Frederik J., Kachanoff, Frank, Kahn, John, Dangol, Apsara Katuwal, Keudel, Oleksandra, Koppel, Lina, Koverola, Mika, Kubin, Emily, Kunnari, Anton, Kutiyski, Yordan, Laguna, Oscar, Leota, Josh, Lermer, Eva, Levy, Jonathan, Levy, Neil, Li, Chunyun, Long, Elizabeth U., Longoni, Chiara, Maglić, Marina, McCashin, Darragh, Metcalf, Alexander L., Mikloušić, Igor, El Mimouni, Soulaimane, Miura, Asako, Molina-Paredes, Juliana, Monroy-Fonseca, César, Morales-Marente, Elena, Moreau, David, Muda, Rafał, Myer, Annalisa, Nash, Kyle, Nesh-Nash, Tarik, Nitschke, Jonas P., Nurse, Matthew S., Ohtsubo, Yohsuke, Oldemburgo de Mello, Victoria, O’Madagain, Cathal, Onderco, Michal, Palacios-Galvez, M. Soledad, Palomäki, Jussi, Pan, Yafeng, Papp, Zsófia, Pärnamets, Philip, Paruzel-Czachura, Mariola, Pavlović, Zoran, Payán-Gómez, César, Perander, Silva, Pitman, Michael Mark, Prasad, Rajib, Pyrkosz-Pacyna, Joanna, Rathje, Steve, Raza, Ali, Rêgo, Gabriel G., Rhee, Kasey, Robertson, Claire E., Rodríguez-Pascual, Iván, Saikkonen, Teemu, Salvador-Ginez, Octavio, Sampaio, Waldir M., Santi, Gaia C., Santiago-Tovar, Natalia, Savage, David, Scheffer, Julian A., Schönegger, Philipp, Schultner, David T., Schutte, Enid M., Scott, Andy, Sharma, Madhavi, Sharma, Pujan, Skali, Ahmed, Stadelmann, David, Stafford, Clara Alexandra, Stanojević, Dragan, Stefaniak, Anna, Sternisko, Anni, Stoica, Augustin, Stoyanova, Kristina K., Strickland, Brent, Sundvall, Jukka, Thomas, Jeffrey P., Tinghög, Gustav, Torgler, Benno, Traast, Iris J., Tucciarelli, Raffaele, Tyrala, Michael, Ungson, Nick D., Uysal, Mete S., Van Lange, Paul A. M., van Prooijen, Jan-Willem, van Rooy, Dirk, Västfjäll, Daniel, Verkoeijen, Peter, Vieira, Joana B., von Sikorski, Christian, Walker, Alexander Cameron, Watermeyer, Jennifer, Wetter, Erik, Whillans, Ashley, Willardt, Robin, Wohl, Michael J. A., Wójcik, Adrian Dominik, Wu, Kaidi, Yamada, Yuki, Yilmaz, Onurcan, Yogeeswaran, Kumar, Ziemer, Carolin-Theresa, Zwaan, Rolf A., and Boggio, Paulo S.

Published
2022
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18. A Shifted Sum for the Congruent Number Problem

Author

Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander

Subjects
Mathematics - Number Theory
Abstract

We introduce a shifted convolution sum that is parametrized by the squarefree natural number $t$. The asymptotic growth of this series depends explicitly on whether or not $t$ is a \emph{congruent number}, an integer that is the area of a rational right triangle. This series presents a new avenue of inquiry for The Congruent Number Problem.

Published
2018

19. The Laplace Transform of the Second Moment in the Gauss Circle Problem

Author

Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander

Subjects
Mathematics - Number Theory
Abstract

The Gauss circle problem concerns the difference $P_2(n)$ between the area of a circle of radius $\sqrt{n}$ and the number of lattice points it contains. In this paper, we study the Dirichlet series with coefficients $P_2(n)^2$, and prove that this series has meromorphic continuation to $\mathbb{C}$. Using this series, we prove that the Laplace transform of $P_2(n)^2$ satisfies $\int_0^\infty P_2(t)^2 e^{-t/X} \, dt = C X^{3/2} -X + O(X^{1/2+\epsilon})$, which gives a power-savings improvement to a previous result of Ivic [Ivic1996]. Similarly, we study the meromorphic continuation of the Dirichlet series associated to the correlations $r_2(n+h)r_2(n)$, where $h$ is fixed and $r_2(n)$ denotes the number of representations of $n$ as a sum of two squares. We use this Dirichlet series to prove asymptotics for $\sum_{n \geq 1} r_2(n+h)r_2(n) e^{-n/X}$, and to provide an additional evaluation of the leading coefficient in the asymptotic for $\sum_{n \leq X} r_2(n+h)r_2(n)$., Comment: Incorporate referees' comments

Published
2017
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20. Second Moments in the Generalized Gauss Circle Problem

Author

Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander

Subjects
Mathematics - Number Theory, 11F30, 11F03, 11E45, 11P21
Abstract

The generalized Gauss circle problem concerns the lattice point discrepancy of large spheres. We study the Dirichlet series associated to $P_k(n)^2$, where $P_k(n)$ is the discrepancy between the volume of the $k$-dimensional sphere of radius $\sqrt{n}$ and the number of integer lattice points contained in that sphere. We prove asymptotics with improved power-saving error terms for smoothed sums, including $\sum P_k(n)^2 e^{-n/X}$ and the Laplace transform $\int_0^\infty P_k(t)^2 e^{-t/X}dt$, in dimensions $k \geq 3$. We also obtain main terms and power-saving error terms for the sharp sums $\sum_{n \leq X} P_k(n)^2$, along with similar results for the sharp integral $\int_0^X P_3(t)^2 dt$. This includes producing the first power-saving error term in mean square for the dimension-three Gauss circle problem., Comment: Now 36 pages + 7 page appendix. To appear in Forum of Mathematics Sigma

Published
2017
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21. Sign Changes of Coefficients and Sums of Coefficients of L-Functions

Author

Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander

Subjects
Mathematics - Number Theory, 11F30
Abstract

We extend the axiomatization for detecting and quantifying sign changes of Meher and Murty to sequences of complex numbers. We further generalize this result when the sequence is comprised of the coefficients of an $L$-function. As immediate applications, we prove that there are sign changes in intervals within sequences of coefficients of GL(2) holomorphic cusp forms, GL(2) Maass forms, and GL(3) Maass forms. Building on previous works by the authors, we prove that there are sign changes in intervals within sequences of partial sums of coefficients of GL(2) holomorphic cusp forms and Maass forms.

Published
2016
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22. Graphs of Large Girth and Surfaces of Large Systole

Author

Petri, Bram and Walker, Alexander

Subjects
Mathematics - Geometric Topology, Mathematics - Combinatorics, Mathematics - Differential Geometry, Mathematics - Number Theory
Abstract

The systole of a hyperbolic surface is bounded by a logarithmic function of its genus. This bound is sharp, in that there exist sequences of surfaces with genera tending to infinity that attain logarithmically large systoles. These are constructed by taking congruence covers of arithmetic surfaces. In this article we provide a new construction for a sequence of surfaces with systoles that grow logarithmically in their genera. We do this by combining a construction for graphs of large girth and a count of the number of $\mathrm{SL}_2(\mathbb{Z})$ matrices with positive entries and bounded trace., Comment: 14 pages, 2 figures

Published
2015

23. Short-Interval Averages of Sums of Fourier Coefficients of Cusp Forms

Author

Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander

Subjects
Mathematics - Number Theory, 11F30
Abstract

Let $f$ be a weight $k$ holomorphic cusp form of level one, and let $S_f(n)$ denote the sum of the first $n$ Fourier coefficients of $f$. In analogy with Dirichlet's divisor problem, it is conjectured that $S_f(X) \ll X^{\frac{k-1}{2} + \frac{1}{4} + \epsilon}$. Understanding and bounding $S_f(X)$ has been a very active area of research. The current best bound for individual $S_f(X)$ is $S_f(X) \ll X^{\frac{k-1}{2} + \frac{1}{3}} (\log X)^{-0.1185}$ from Wu. Chandrasekharan and Narasimhan showed that the Classical Conjecture for $S_f(X)$ holds on average over intervals of length $X$. Jutila improved this result to show that the Classical Conjecture for $S_f(X)$ holds on average over short intervals of length $X^{\frac{3}{4} + \epsilon}$. Building on the results and analytic information about $\sum \lvert S_f(n) \rvert^2 n^{-(s + k - 1)}$ from our recent work, we further improve these results to show that the Classical Conjecture for $S_f(X)$ holds on average over short intervals of length $X^{\frac{2}{3}}(\log X)^{\frac{1}{6}}$., Comment: To Appear in the Journal of Number Theory

Published
2015
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24. The Second Moment of Sums of Coefficients of Cusp Forms

Author

Hulse, Thomas A., Kuan, Chan Ieong, Lowry-Duda, David, and Walker, Alexander

Subjects
Mathematics - Number Theory, 11F30
Abstract

Let $f$ and $g$ be weight $k$ holomorphic cusp forms and let $S_f(n)$ and $S_g(n)$ denote the sums of their first $n$ Fourier coefficients. Hafner and Ivic [HI], building on Chandrasekharan and Narasimhan [CN], proved asymptotics for $\sum_{n \leq X} \lvert S_f(n) \rvert^2$ and proved that the Classical Conjecture, that $S_f(X) \ll X^{\frac{k-1}{2} + \frac{1}{4} + \epsilon}$, holds on average over long intervals. In this paper, we introduce and obtain meromorphic continuations for the Dirichlet series $D(s, S_f \times S_g) = \sum S_f(n)\overline{S_g(n)} n^{-(s+k-1)}$ and $D(s, S_f \times \overline{S_g}) = \sum_n S_f(n)S_g(n) n^{-(s + k - 1)}$. Using these meromorphic continuations, we prove asymptotics for the smoothed second moment sums $\sum S_f(n)\overline{S_g(n)} e^{-n/X}$, proving a smoothed generalization of [HI]. We also attain asymptotics for analogous smoothed second moment sums of normalized Fourier coefficients, proving smoothed generalizations of what would be attainable from [CN]. Our methodology extends to a wide variety of weights and levels, and comparison with [CN] indicates very general cancellation between the Rankin-Selberg $L$-function $L(s, f\times g)$ and shifted convolution sums of the coefficients of $f$ and $g$. In forthcoming works, the authors apply the results of this paper to prove the Classical Conjecture on $\lvert S_f(n) \rvert^2$ is true on short intervals, and to prove sign change results on $\{S_f(n)\}_{n \in \mathbb{N}}$., Comment: To appear in the Journal of Number Theory

Published
2015
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25. Semiparametric Allocation of Subjects to Cohort Strata.

Author

Walker, Alexander M., Russo, Massimiliano, Schneeweiss, Maria C., and Glynn, Robert J.

Abstract

Background: We illustrate a method for stratum assignment in small cohort studies that avoids modeling assumptions. Methods: Off-the-shelf software (rgenoud) made stratum assignments to minimize a loss function built on within-stratum and populationadjusted Euclidean distances. Results: In 100 trials using simulated data of 300 records with a binary treatment and four dissimilar covariate treatment predictors, minimizing a loss based on Euclidean distance reduced covariate imbalance by a median of 99%. Stratification by propensity score and weighting records by the inverse of their probability of treatment reduced imbalance by 76%-89% and 83%-94%, respectively. Loss minimization applied to a cohort of 361 children undergoing immunotherapy achieved nearly complete elimination of covariate differences for important treatment predictors. Conclusion: With the availability of semiparametric stratumassignment algorithms, analysts can tailor loss functions to meet design goals. Here, a loss function that emphasized covariate balance performed well under limited testing. [ABSTRACT FROM AUTHOR]

Published
2024
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26. Host ANP32A mediates the assembly of the influenza virus replicase

Author

Carrique, Loïc, Fan, Haitian, Walker, Alexander P., Keown, Jeremy R., Sharps, Jane, Staller, Ecco, and Barclay, Wendy S.

Subjects
RNA polymerases -- Physiological aspects, Influenza viruses -- Physiological aspects -- Genetic aspects, Environmental issues, Science and technology, Zoology and wildlife conservation
Abstract

Aquatic birds represent a vast reservoir from which new pandemic influenza A viruses can emerge.sup.1. Influenza viruses contain a negative-sense segmented RNA genome that is transcribed and replicated by the viral heterotrimeric RNA polymerase (FluPol) in the context of viral ribonucleoprotein complexes.sup.2,3. RNA polymerases of avian influenza A viruses (FluPolA) replicate viral RNA inefficiently in human cells because of species-specific differences in acidic nuclear phosphoprotein 32 (ANP32), a family of essential host proteins for FluPol activity.sup.4. Host-adaptive mutations, particularly a glutamic-acid-to-lysine mutation at amino acid residue 627 (E627K) in the 627 domain of the PB2 subunit, enable avian FluPolA to overcome this restriction and efficiently replicate viral RNA in the presence of human ANP32 proteins. However, the molecular mechanisms of genome replication and the interplay with ANP32 proteins remain largely unknown. Here we report cryo-electron microscopy structures of influenza C virus polymerase (FluPolC) in complex with human and chicken ANP32A. In both structures, two FluPolC molecules form an asymmetric dimer bridged by the N-terminal leucine-rich repeat domain of ANP32A. The C-terminal low-complexity acidic region of ANP32A inserts between the two juxtaposed PB2 627 domains of the asymmetric FluPolA dimer, suggesting a mechanism for how the adaptive PB2(E627K) mutation enables the replication of viral RNA in mammalian hosts. We propose that this complex represents a replication platform for the viral RNA genome, in which one of the FluPol molecules acts as a replicase while the other initiates the assembly of the nascent replication product into a viral ribonucleoprotein complex. Structural and biochemical studies of influenza virus RNA polymerase in complex with host acidic nuclear phosphoprotein 32 (ANP32) show how ANP32-mediated polymerase dimerization enables the replication of influenza viral RNA in a host-dependent manner., Author(s): Loïc Carrique [sup.1] , Haitian Fan [sup.2] , Alexander P. Walker [sup.2] , Jeremy R. Keown [sup.1] , Jane Sharps [sup.2] , Ecco Staller [sup.3] [sup.5] , Wendy S. [...]

Published
2020
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27. Structures of influenza A virus RNA polymerase offer insight into viral genome replication

Author

Fan, Haitian, Walker, Alexander P., Carrique, Loïc, Keown, Jeremy R., Serna Martin, Itziar, Karia, Dimple, and Sharps, Jane

Subjects
RNA polymerases -- Structure, Influenza viruses -- Analysis -- Genetic aspects, Environmental issues, Science and technology, Zoology and wildlife conservation
Abstract

Influenza A viruses are responsible for seasonal epidemics, and pandemics can arise from the transmission of novel zoonotic influenza A viruses to humans.sup.1,2. Influenza A viruses contain a segmented negative-sense RNA genome, which is transcribed and replicated by the viral-RNA-dependent RNA polymerase (FluPol.sub.A) composed of PB1, PB2 and PA subunits.sup.3-5. Although the high-resolution crystal structure of FluPol.sub.A of bat influenza A virus has previously been reported.sup.6, there are no complete structures available for human and avian FluPol.sub.A. Furthermore, the molecular mechanisms of genomic viral RNA (vRNA) replication--which proceeds through a complementary RNA (cRNA) replicative intermediate, and requires oligomerization of the polymerase.sup.7-10--remain largely unknown. Here, using crystallography and cryo-electron microscopy, we determine the structures of FluPol.sub.A from human influenza A/NT/60/1968 (H3N2) and avian influenza A/duck/Fujian/01/2002 (H5N1) viruses at a resolution of 3.0-4.3 Å, in the presence or absence of a cRNA or vRNA template. In solution, FluPol.sub.A forms dimers of heterotrimers through the C-terminal domain of the PA subunit, the thumb subdomain of PB1 and the N1 subdomain of PB2. The cryo-electron microscopy structure of monomeric FluPol.sub.A bound to the cRNA template reveals a binding site for the 3' cRNA at the dimer interface. We use a combination of cell-based and in vitro assays to show that the interface of the FluPol.sub.A dimer is required for vRNA synthesis during replication of the viral genome. We also show that a nanobody (a single-domain antibody) that interferes with FluPol.sub.A dimerization inhibits the synthesis of vRNA and, consequently, inhibits virus replication in infected cells. Our study provides high-resolution structures of medically relevant FluPol.sub.A, as well as insights into the replication mechanisms of the viral RNA genome. In addition, our work identifies sites in FluPol.sub.A that could be targeted in the development of antiviral drugs. Structures of RNA polymerase of human and avian influenza A viruses reveal that the interface of the RNA polymerase dimer is required to initiate viral RNA synthesis in viral genome replication., Author(s): Haitian Fan [sup.1] , Alexander P. Walker [sup.1] , Loïc Carrique [sup.2] , Jeremy R. Keown [sup.2] , Itziar Serna Martin [sup.1] [sup.2] [sup.6] , Dimple Karia [sup.2] , [...]

Published
2019
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31. Arithmetic Properties of Picard-Fuchs Equations and Holonomic Recurrences

Author

Li, Zane Kun and Walker, Alexander W.

Subjects
Mathematics - Number Theory, 11F03, 14H52
Abstract

The coefficient series of the holomorphic Picard-Fuchs differential equation associated with the periods of elliptic curves often have surprising number-theoretic properties. These have been widely studied in the case of the torsion-free, genus zero congruence subgroups of index 6 and 12 (e.g. the Beauville families). Here, we consider arithmetic properties of the Picard-Fuchs solutions associated to general elliptic families, with a particular focus on the index 24 congruence subgroups. We prove that elliptic families with rational parameters admit linear reparametrizations such that their associated Picard-Fuchs solutions lie in Z[[t]]. A sufficient condition is given such that the same holds for holomorphic solutions at infinity. An Atkin-Swinnerton-Dyer congruence is proven for the coefficient series attached to \Gamma_1(7). We conclude with a consideration of asymptotics, wherein it is proved that many coefficient series satisfy asymptotic expressions of the form u_n \sim \ell \lambda^n/n. Certain arithmetic results extend to the study of general holonomic recurrences., Comment: 21 pages, to appear in the Journal of Number Theory

Published
2013

36. Tutors' Responses to Student Disclosures: From "Suicidal Ideation" to "Feeling a Little Stressed".

Author

Walker, Alexander, Tait-McCutcheon, Sandi L., and Gilbert, Amanda

Subjects
LONELINESS, SUICIDAL ideation, UNIVERSITIES & colleges, DISCLOSURE, TUTORS & tutoring, THEMATIC analysis
Abstract

Tutors in higher education are receiving and responding to student disclosures that include racism, anxiety, loneliness, legal disputes, family upheavals, physical, emotional, and mental health, bereavement, legal battles, and harassment. In many cases, this caring aspect of the tutor role is not acknowledged, allocated time in job descriptions, or accurately remunerated. This qualitative study explored how tutors experienced and managed student disclosures, the personal and professional impact of responding to disclosures, and how tutors believed they could be better supported. Data was collected from two cohorts of participants tutoring at a University in Aotearoa New Zealand. using interviews and questionnaires and analysed by reflexive thematic analysis. Our findings showed that our participants believed they were positioned vulnerably between a rock and a hard place. At the rock, tutors were told to follow university guidelines and refer distressed students to over-loaded course coordinators or over-subscribed support services. At the hard place, tutors were often the first to be disclosed to, because of their front-facing positioning at the university and once they had heard the disclosure felt it was unethical not to try and help. Tutors believed they could assist students with personal challenges if their precarious positioning within the university was protected and strengthened and if appropriate support was provided by their university through training, time, and remuneration. Findings have implications for higher education providers to reconsider how tutors are supported to support students. [ABSTRACT FROM AUTHOR]

Published
2023
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39. Characterization of the SARS-CoV-2 ExoN (nsp14ExoN–nsp10) complex: implications for its role in viral genome stability and inhibitor identification

Author

Baddock, Hannah T, primary, Brolih, Sanja, additional, Yosaatmadja, Yuliana, additional, Ratnaweera, Malitha, additional, Bielinski, Marcin, additional, Swift, Lonnie P, additional, Cruz-Migoni, Abimael, additional, Fan, Haitian, additional, Keown, Jeremy R, additional, Walker, Alexander P, additional, Morris, Garrett M, additional, Grimes, Jonathan M, additional, Fodor, Ervin, additional, Schofield, Christopher J, additional, Gileadi, Opher, additional, and McHugh, Peter J, additional

Published
2022
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