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We improve the uniformity in the asymptotic Chebotarev density theorem for Galois extensions of number fields satisfying Artin's holomorphy conjecture. Using nonabelian base change, this yields an unconditional improvement to the uniformity in the Chebotarev density theorem along with the first theoretical improvement over Weiss's bound for the least norm of an unramified prime ideal in the Chebotarev density theorem., Comment: 35 pages

We combine the relative trace formula with analytic methods to obtain zero density estimate for $L$-functions in various families of automorphic representations for $\mathrm{GL}(m)$. Applications include strong bounds for the average analytic rank of these $L$-functions at the central point and average equidistribution results for the imaginary parts of the zeros., Comment: 21 pages

This paper presents the 3D soundfield synthesis of the pressure field radiated by directional acoustic sources using both the multimodal method and higher-order ambisonics (HOA). Ambisonics is a technique for encoding and reproducing measured or modeled (virtual) sound pressure field, based on a decomposition of the acoustic field over spherical harmonics. The directional source considered in this work is an acoustic horn excited by a flat piston. The free-field radiation from this horn is first modeled accurately over a wide frequency range using the multimodal method, which requires relatively low computational resources. This radiated pressure field, collected on a dual-layer sphere of virtual sensors distributed over a Lebedev geometry, allows its projection into the ambisonic domain. The pressure field is then synthesized in the laboratory's 3D 5th order HOA spatialization sphere, which consists of fifty-six loudspeakers. This offers the ability of listening to the radiated sound using a higher-order ambisonic synthesis of a 'virtual' source before it is manufactured. To qualitatively evaluate the performance of the proposed procedure, the transfer function of the synthesized horn is measured around the listening point within the spatialization sphere., Comment: Internoise 2024, Aug 2024, Nantes (France), France

Let $L(s,\pi)=\sum_{n=1}^{\infty}\lambda_{\pi}(n)n^{-s}$ be an $L$-function that satisfies a weak form of the generalized Ramanujan conjecture. We prove that large partial sums of $\lambda_{\pi}(n)$ strongly repel the low-lying zeros of $L(s,\pi)$ away from the critical line. Our results extend and quantitatively improve preceding work of Granville and Soundararajan., Comment: 23 pages

For certain families of $L$-functions, we prove that if each $L$-function in the family has only real zeros in a fixed yet arbitrarily small neighborhood of $s=1$, then one may considerably improve upon the known results on Landau-Siegel zeros. Sarnak and the third author proved a similar result under much more restrictive hypotheses., Comment: 7 pages. Referee comments incorporated

Let $\chi$ be an idele class character over a number field $F$, and let $\pi,\pi'$ be non-dihedral twist-inequivalent cuspidal automorphic representations of $\mathrm{GL}_2(\mathbb{A}_F)$. We prove the following results. 1. If $m,n\geq 0$ are integers, $m+n\geq 1$, $F$ is totally real, $\chi$ corresponds with a ray class character, and $\pi,\pi'$ correspond with primitive non-CM holomorphic Hilbert cusp forms, then the Rankin-Selberg $L$-function $L(s,\mathrm{Sym}^m(\pi)\times(\mathrm{Sym}^n(\pi')\otimes\chi))$ has a standard zero-free region with no exceptional Landau-Siegel zero. When $m,n\geq 1$ and $m+n\geq 4$, this is new even for $F=\mathbb{Q}$. As an application, we establish the strongest known unconditional effective rates of convergence in the Sato-Tate distribution for $\pi$ and the joint Sato-Tate distribution for $\pi$ and $\pi'$. 2. The Rankin-Selberg $L$-function $L(s,\mathrm{Sym}^2(\pi)\times(\mathrm{Sym}^2 (\pi')\otimes\chi))$ has a standard zero-free region with no exceptional Landau-Siegel zero. Until now, this was only known when $\pi=\pi'$, $\pi$ is self-dual, and $\chi$ is trivial., Comment: 22 pages

We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual $\mathrm{GL}_2$ Hecke-Maass newforms over $\mathbb{Q}$ as the level and Laplace eigenvalue vary jointly. The second is a nonsplit analogue wherein almost all restrictions of Hilbert (respectively Bianchi) Hecke-Maass cusp forms to the modular surface dissipate as their Laplace eigenvalues grow., Comment: 28 pages. arXiv admin note: substantial text overlap with arXiv:2103.05634

Let $\pi$ and $\pi'$ be cuspidal automorphic representations of $\mathrm{GL}(n)$ and $\mathrm{GL}(n')$ with unitary central characters. We establish a new zero-free region for all $\mathrm{GL}(1)$-twists of the Rankin-Selberg $L$-function $L(s,\pi\times\pi')$, generalizing Siegel's celebrated work on Dirichlet $L$-functions. As an application, we prove the first unconditional Siegel-Walfisz theorem for the Dirichlet coefficients of $-L'(s,\pi\times\pi')/L(s,\pi\times\pi')$. Also, for $n\leq 8$, we extend the region of holomorphy and nonvanishing for the twisted symmetric power $L$-functions $L(s,\pi,\mathrm{Sym}^n\otimes\chi)$ of any cuspidal automorphic representation of $\mathrm{GL}(2)$., Comment: 21 pages, LaTeX2e; v2: updated Section 3 and the Remark below Theorem 1.1; v3: updated Section 1, added Theorem 2.2 and Section 8, added the Remark below the proof of Proposition 4.4; v4: updated the end of Section 1, added Section 4 (part of which was formerly Section 5.2); v5: updated Section 1; v6: updated Section 5

We make explicit Bombieri's refinement of Gallagher's log-free "large sieve density estimate near $\sigma = 1$" for Dirichlet $L$-functions. We use this estimate and recent work of Green to prove that if $N\geq 2$ is an integer, $A\subseteq\{1,\ldots,N\}$, and for all primes $p$ no two elements in $A$ differ by $p-1$, then $|A|\ll N^{1-1/10^{18}}$. This strengthens a theorem of S\'ark\"ozy., Comment: 24 pages. v4: Incorporates referee comments

We prove a highly uniform version of the prime number theorem for a certain class of $L$-functions. The range of $x$ depends polynomially on the analytic conductor, and the error term is expressed in terms of an optimization problem depending explicitly on the available zero-free region. The class contains the Rankin-Selberg $L$-function $L(s,\pi \times \pi')$ associated to cuspidal automorphic representations $\pi$ and $\pi'$ of $\mathrm{GL}_{m}$ and $\mathrm{GL}_{m'}$, respectively. Our main result implies the first uniform prime number theorems for such $L$-functions (with analytic conductor uniformity) in complete generality., Comment: 16 pages. Incorporates referee comments. Theorem 2.6 is improved

We show that Landau-Siegel zeros for Dirichlet $L$-functions do not exist or quantum unique ergodicity for $\mathrm{GL}_2$ Hecke-Maass newforms holds with an effective rate of convergence. This follows from a more general result: Landau-Siegel zeros of Dirichlet $L$-functions repel the zeros of all other automorphic $L$-functions from the line $\mathrm{Re}(s)=1$., Comment: 11 pages

Let $E/\mathbb{Q}$ be an elliptic curve that has complex multiplication (CM) by an imaginary quadratic field $K$. For a prime $p$, there exists $\theta_p \in [0, \pi]$ such that $p+1-\#E(\mathbb{F}_p) = 2\sqrt{p} \cos \theta_p$. Let $x>0$ be large, and let $I\subseteq[0,\pi]$ be a subinterval. We prove that if $\delta>0$ and $\theta>0$ are fixed numbers such that $\delta+\theta<\frac{5}{24}$, $x^{1-\delta}\leq h\leq x$, and $|I|\geq x^{-\theta}$, then \[ \frac{1}{h}\sum_{\substack{x < p \le x+h \\ \theta_p \in I}}\log{p}\sim \frac{1}{2}\mathbf{1}_{\frac{\pi}{2}\in I}+\frac{|I|}{2\pi}, \] where $\mathbf{1}_{\frac{\pi}{2}\in I}$ equals 1 if $\frac{\pi}{2}\in I$ and $0$ otherwise. We also discuss an extension of this result to the distribution of the Fourier coefficients of holomorphic cuspidal CM newforms., Comment: 10 pages, significant revision after referee comments

We establish a result of Bombieri-Vinogradov type for the Dirichlet coefficients at prime ideals of the standard $L$-function associated to a self-dual cuspidal automorphic representation $\pi$ of $\mathrm{GL}_n$ over a number field $F$ which is not a quadratic twist of itself. Our result does not rely on any unproven progress towards the generalized Ramanujan conjecture or the nonexistence of Landau-Siegel zeros. In particular, when $\pi$ is fixed and not equal to a quadratic twist of itself, we prove the first unconditional Siegel-type lower bound for the twisted $L$-values $|L(1,\pi\otimes\chi)|$ in the $\chi$-aspect, where $\chi$ is a primitive quadratic Hecke character over $F$. Our result improves the levels of distribution in other works that relied on these unproven hypotheses. As applications, when $n=2,3,4$, we prove a $\mathrm{GL}_n$ analogue of the Titchmarsh divisor problem and a nontrivial bound for a certain $\mathrm{GL}_n\times\mathrm{GL}_2$ shifted convolution sum., Comment: 40 pages. Added Section 3. Extended discussion of the Siegel zero problem in Section 4

Let $\mathfrak{F}_n$ be the set of all cuspidal automorphic representations $\pi$ of $\mathrm{GL}_n$ with unitary central character over a number field $F$. We prove the first unconditional zero density estimate for the set $\mathcal{S}=\{L(s,\pi\times\pi')\colon\pi\in\mathfrak{F}_n\}$ of Rankin-Selberg $L$-functions, where $\pi'\in\mathfrak{F}_{n'}$ is fixed. We use this density estimate to establish (i) a hybrid-aspect subconvexity bound at $s=\frac{1}{2}$ for almost all $L(s,\pi\times\pi')\in \mathcal{S}$, (ii) a strong on-average form of effective multiplicity one for almost all $\pi\in\mathfrak{F}_n$, and (iii) a positive level of distribution for $L(s,\pi\times\tilde{\pi})$, in the sense of Bombieri-Vinogradov, for each $\pi\in\mathfrak{F}_n$., Comment: 32 pages. Significant revision based on referee comments

We prove an analogue of Selberg's zero density estimate for $\zeta(s)$ that holds for any $\mathrm{GL}_2$ $L$-function. We use this estimate to study the distribution of the vector of fractional parts of $\gamma\mathbf{\alpha}$, where $\mathbf{\alpha}\in\mathbb{R}^n$ is fixed and $\gamma$ varies over the imaginary parts of the nontrivial zeros of a $\mathrm{GL}_2$ $L$-function., Comment: 25 pages

Let $\pi$ be a unitary cuspidal automorphic representation of $\mathrm{GL}_n$ over a number field, and let $\tilde{\pi}$ be contragredient to $\pi$. We prove effective upper and lower bounds of the correct order in the short interval prime number theorem for the Rankin-Selberg $L$-function $L(s,\pi\times\tilde{\pi})$, extending the work of Hoheisel and Linnik. Along the way, we prove for the first time that $L(s,\pi\times\widetilde{\pi})$ has an unconditional standard zero-free region apart from a possible Landau-Siegel zero., Comment: 23 pages. Incorporates referee comments

We use Levinson's method and the work of Blomer and Harcos on the $\mathrm{GL}_2$ shifted convolution problem to prove that at least 6.96% of the zeros of the L-function of any holomorphic or Maass cusp form lie on the critical line., Comment: 15 pages

Let $f(z)=\sum_{n=1}^{\infty} a_f(n)e^{2\pi i n z}$ be a non-CM holomorphic cupsidal newform of trivial nebentypus and even integral level $k\geq 2$. Deligne's proof of the Weil conjectures shows that $|a_f(p)|\leq 2p^{\frac{k-1}{2}}$ for all primes $p$. We prove for 100% of primes $p$ that $2p^{\frac{k-1}{2}}\frac{\log\log p}{\sqrt{\log p}}<|a_f(p)|<\lfloor 2p^{\frac{k-1}{2}}\rfloor$. Our proof gives an effective upper bound for the size of the exceptional set. The lower bound shows that the Atkin-Serre conjecture is satisfied for 100% of primes, and the upper bound shows that $|a_f(p)|$ is as large as possible (i.e., $p$ is extremal for $f$) for 0% of primes. Our proofs use the effective form of the Sato-Tate conjecture proved by the second author, which relies on the recent proof of the automorphy of the symmetric powers of $f$ due to Newton and Thorne., Comment: Condition requiring squarefree level is removed. Title change

We prove effective forms of the Sato-Tate conjecture for holomorphic cuspidal newforms which improve on the author's previous work (solo and joint with Lemke Oliver). We also prove an effective form of the joint Sato-Tate distribution for two twist-inequivalent newforms. Our results are unconditional because of recent work of Newton and Thorne., Comment: 19 pages. The condition that the level be squarefree is removed

We investigate Riemann's xi function $\xi(s):=\frac{1}{2}s(s-1)\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$ (here $\zeta(s)$ is the Riemann zeta function). The Riemann Hypothesis (RH) asserts that if $\xi(s)=0$, then $\mathrm{Re}(s)=\frac{1}{2}$. P\'olya proved that RH is equivalent to the hyperbolicity of the Jensen polynomials $J^{d,n}(X)$ constructed from certain Taylor coefficients of $\xi(s)$. For each $d\geq 1$, recent work proves that $J^{d,n}(X)$ is hyperbolic for sufficiently large $n$. Here we make this result effective. Moreover, we show how the low-lying zeros of the derivatives $\xi^{(n)}(s)$ influence the hyperbolicity of $J^{d,n}(X)$., Comment: 13 pages. This revision represents a major revision of the previous version. The exposition has been improved and many clarifications have been added. Moreover, Theorem 1.1 has been improved

Given a nontrivial finite group $G$, we prove the first zero density estimate for families of Dedekind zeta functions associated to Galois extensions $K/\mathbb{Q}$ with $\mathrm{Gal}(K/\mathbb{Q})\cong G$ that does not rely on unproven progress towards the strong form of Artin's conjecture. We use this to remove the hypothesis of the strong Artin conjecture from the work of Pierce, Turnage-Butterbaugh, and Wood on the average error in the Chebotarev density theorem and $\ell$-torsion in ideal class groups., Comment: Considerably streamlined, small refinements to Theorems 1.1 and 1.2. 14 pages

Let $\tau(n)$ be Ramanujan's tau function, defined by the discriminant modular form \[ \Delta(z) = q\prod_{j=1}^{\infty}(1-q^{j})^{24}\ =\ \sum_{n=1}^{\infty}\tau(n) q^n \,,q=e^{2\pi i z} \] (this is the unique holomorphic normalized cuspidal newform of weight 12 and level 1). Lehmer's conjecture asserts that $\tau(n)\neq 0$ for all $n\geq 1$; since $\tau(n)$ is multiplicative, it suffices to study primes $p$ for which $\tau(p)$ might possibly be zero. Assuming standard conjectures for the twisted symmetric power $L$-functions associated to $\tau$ (including GRH), we prove that if $x\geq 10^{50}$, then \[ \#\{x < p\leq 2x: \tau(p) = 0\} \leq 1.22 \times 10^{-5} \frac{x^{3/4}}{\sqrt{\log x}},\] a substantial improvement on the implied constant in previous work. To achieve this, under the same hypotheses, we prove an explicit version of the Sato-Tate conjecture for primes in arithmetic progressions., Comment: 16 pages, fixed typographical errors and minor computational details. To be published in the International Journal of Number Theory

Let $\mathfrak{F}_n$ be the set of all cuspidal automorphic representations $\pi$ of $\mathrm{GL}_n$ over a number field with unitary central character. We prove two unconditional large sieve inequalities for the Hecke eigenvalues of $\pi\in\mathfrak{F}_n$, one on the integers and one on the primes. The second leads to the first unconditional zero density estimate for the family of $L$-functions $L(s,\pi)$ associated to $\pi\in\mathfrak{F}_n$, which we make log-free. As an application of the zero density estimate, we prove a hybrid subconvexity bound for $L(\frac{1}{2},\pi)$ for a density one subset of $\pi\in\mathfrak{F}_n$., Comment: 17 pages. Incorporates referee comments

Saccharomyces cerevisiae target of rapamycin (TOR) complex 2 (TORC2) is an essential regulator of plasma membrane lipid and protein homeostasis. How TORC2 activity is modulated in response to changes in the status of the cell envelope is unclear. Here we document that TORC2 subunit Avo2 is a direct target of Slt2, the mitogen-activated protein kinase (MAPK) of the cell wall integrity pathway. Activation of Slt2 by overexpression of a constitutively active allele of an upstream Slt2 activator (Pkc1) or by auxin-induced degradation of a negative Slt2 regulator (Sln1) caused hyperphosphorylation of Avo2 at its MAPK phosphoacceptor sites in a Slt2-dependent manner and diminished TORC2-mediated phosphorylation of its major downstream effector, protein kinase Ypk1. Deletion of Avo2 or expression of a phosphomimetic Avo2 allele rendered cells sensitive to two stresses (myriocin treatment and elevated exogenous acetic acid) that the cell requires Ypk1 activation by TORC2 to survive. Thus, Avo2 is necessary for optimal TORC2 activity, and Slt2-mediated phosphorylation of Avo2 down-regulates TORC2 signaling. Compared with wild-type Avo2, phosphomimetic Avo2 shows significant displacement from the plasma membrane, suggesting that Slt2 inhibits TORC2 by promoting Avo2 dissociation. Our findings are the first demonstration that TORC2 function is regulated by MAPK-mediated phosphorylation., Comment: This work was supported by National Institutes of Health (NIH) Predoctoral Traineeship GM07232 and a University of California at Berkeley MacArthur and Lakhan-Pal Graduate Fellowship to K.L.L., Erwin Schroedinger Fellowship J3787-B21 from the Austrian Science Fund to AE-A, Marie Sklodowska-Curie Action H2020-MSCA-IF-2016 InsiliCardio, GA 75083 to CMA, and NIH R01 research grant GM21841 to JT

To observe internalization of the yeast pheromone receptor Ste2 by fluorescence microscopy in live cells in real time, we visualized only those molecules present at the cell surface at the time of agonist engagement (rather than the total cellular pool) by tagging this receptor at its N-terminus with an exocellular fluorogen-activating protein (FAP). A FAP is a single-chain antibody engineered to bind tightly a nonfluorescent, cell-impermeable dye (fluorogen), thereby generating a fluorescent complex. The utility of FAP tagging to study trafficking of integral membrane proteins in yeast, which possesses a cell wall, had not been examined previously. A diverse set of signal peptides and propeptide sequences were explored to maximize expression. Maintenance of the optimal FAP-Ste2 chimera intact required deletion of two, paralogous, glycosylphosphatidylinositol (GPI)-anchored extracellular aspartyl proteases (Yps1 and Mkc7). FAP-Ste2 exhibited a much brighter and distinct plasma membrane signal than Ste2-GFP or Ste2-mCherry yet behaved quite similarly. Using FAP-Ste2, new information was obtained about the mechanism of its internalization, including novel insights about the roles of the cargo-selective endocytic adaptors Ldb19/Art1, Rod1/Art4, and Rog3/Art7., Comment: This work was supported by Erwin Schroedinger Fellowship J3787-B21 from the Austrian Science Fund and by National Institutes of Health (NIH) R01 Research Grant GM21841. Additionally, this project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Action H2020-MSCA-IF-2016 InsiliCardio, GA No. 750835

Let $\pi$ and $\pi_0$ be unitary cuspidal automorphic representations. We prove log-free zero density estimates for Rankin-Selberg $L$-functions of the form $L(s,\pi\times\pi_0)$, where $\pi$ varies in a given family and $\pi_0$ is fixed. These estimates are unconditional in many cases of interest; they hold in full generality assuming an average form of the generalized Ramanujan conjecture. We consider applications of these estimates related to mass equidistribution for Hecke-Maass forms, the rarity of Landau-Siegel zeros of Rankin-Selberg $L$-functions, the Chebotarev density theorem, and $\ell$-torsion in class groups of number fields., Comment: 53 pages. Farrell Brumley added as coauthor. Added two appendices, one of which is authored by Colin Bushnell and Guy Henniart. Theorem 1.3 added, leads to cleaner versions of Theorems 1.2 and 1.4

We describe a new method to obtain weak subconvexity bounds for $L$-functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all automorphic $L$-functions and (with mild restrictions) the Rankin-Selberg $L$-functions attached to two automorphic representations. The proof relies on a new unconditional log-free zero density estimate for Rankin-Selberg $L$-functions., Comment: 25 pages. Appendix by Farrell Brumley. Referee comments incorporated

We establish an unconditional effective Chebotarev density theorem that improves uniformly over the well-known result of Lagarias and Odlyzko. As a consequence, we give a new asymptotic form of the Chebotarev density theorem that can count much smaller primes with arbitrary log-power savings, even in the case where a Landau-Siegel zero is present. Our main theorem interpolates the strongest unconditional upper bound for the least prime ideal with a given Artin symbol as well as the Chebotarev analogue of the Brun-Titchmarsh theorem proved by the authors. We also present a new application of our main result that exhibits considerable gains over earlier versions of the Chebotarev density theorem. If $f$ is a positive definite primitive binary quadratic form then we count lattice points $(u,v) \in \mathbb{Z}^2$ such that $f(u,v)$ is prime and $u, v$ have no prime factors $\leq z$ with uniformity in $z$ and the discriminant of $f$., Comment: 26 pages; v3 intro revised and application added in Sections 6 and 7; typos corrected