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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

7. 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

9. 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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11. 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

17. 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

18. Insights into viral RNA synthesis by the influenza A virus and SARS-CoV-2 RNA polymerases

Author

Walker, Alexander and Fodor, Ervin

Abstract

Influenza A virus and SARS-CoV-2 are RNA viruses which cause severe respiratory disease and death in humans. Both encode RNA-dependent RNA polymerases (RdRps), which are responsible for synthesising viral RNA as part of a larger complex of viral proteins; for influenza A virus this complex is called a ribonucleoprotein (RNP), and for SARS-CoV-2 the replication- transcription complex (RTC). In this work I elucidate mechanisms used by influenza A virus and SARS-CoV-2 to synthesise viral RNA. I first present evidence that the influenza A virus RdRp maintains the structural integrity of RNPs during transcription by binding to the 3' end of viral genomic RNA. I then go on to demonstrate that in order to initiate viral RNA synthesis, the influenza A virus RdRp requires trans-activation through dimerization. Furthermore, I show that the influenza A virus RdRp co-opts the host protein ANP32A to help it form a second structurally-distinct dimer, which has the role of encapsidating nascent viral RNA into progeny RNPs. Collectively, these findings allow me to present a more detailed molecular model for how influenza viral RNA is synthesised and assembled into new RNPs. One role of the influenza A virus RNP is to hide highly immunogenic viral RNA from cellular innate immune receptors such as RIG-I. The SARS-CoV-2 RTC instead synthesises 7- methylguanosine (m⁷G)-capped viral RNA which does not activate RIG-I. In this work I also show that one of the domains in the SARS-CoV-2 RdRp is a guanylyltransferase enzyme, which resolves a missing link in the mechanism of coronavirus m⁷G cap synthesis. Together, these studies improve understanding of the diverse mechanisms used by RNA viruses to synthesise viral RNA, and identify multiple functionally important sites on the influenza A virus and SARS- CoV-2 RdRps which could be exploited for future antiviral strategies.

Published
2021

19. 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

22. 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

24. 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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25. 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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27. 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

31. 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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32. 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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38. Moral Narratives Workshop Proceedings

Author

Kim, Judy Sein, primary, Bennett, Jessica, additional, chen, janice, additional, Coman, Alin, additional, Currie, Gregory, additional, Dahlstrom, Michael, additional, De Brigard, Felipe, additional, Dennis, Amanda, additional, Dewey, Aliya, additional, Eden, Allison, additional, Fernández-Miranda, Gabriela, additional, Flores, Carolina, additional, Fowler, Zoe, additional, Fraser, Rachel, additional, Gantman, Ana P., additional, Green, Melanie C., additional, Hadjiandreou, Eliana, additional, Helton, Grace, additional, Heyman, Gail D., additional, Jordan, Jillian, additional, Karg, Simon Tobias, additional, Kronfeld, Maya, additional, Kukla, Quill, additional, Lackey, Jennifer, additional, Lagnado, David, additional, Lombrozo, Tania, additional, McLean, Kate C., additional, Pasupathi, Monisha, additional, Prosser, Annayah Miranda Beatrice, additional, Rea, Michael, additional, Rohde, Hannah, additional, Singh, Manvir, additional, Sinnott-Armstrong, Walter, additional, Walker, Alexander C., additional, Wodak, Ruth, additional, Wilkins, Lauren, additional, and Crockett, Molly, additional

Published
2023
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41. 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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42. 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

43. 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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44. 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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47. Qualitative emphysema and risk of COPD hospitalization in a multicenter CT lung cancer screening cohort study

Author

Gazourian, Lee, Thedinger, William B., Regis, Shawn M., Pagura, Elizabeth J., Price, Lori Lyn, Gawlik, Melissa, Stefanescu, Cristina F., Lamb, Carla, Rieger-Christ, Kimberly M., Singh, Harpreet, Casasola, Marcel, Walker, Alexander R., Rupal, Arashdeep, Patel, Avignat S., Come, Carolyn E., Sanayei, Ava M., Long, William P., Rizzo, Giulia S., McKee, Andrea B., Washko, George R., San Jose Estepar, Raul, Wald, Christoph, McKee, Brady J., Thomson, Carey C., and Liesching, Timothy N.

Published
2021
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