| Date: | February 27, 2024 |
| Time: | 09:45am |
| Location: | BLOC 302 |
| Speaker: | Sumit Kumar, Alfréd Rényi Institute of Mathematics |
| Title: | Hybrid level aspect subconvexity for L-functions |
| Abstract: | Level aspect subconvextiy problem has always been elusive in number theory. In this talk we discuss history of the problem and prove the level aspect subconvexity for degree six GL(3) × Gl(2) Rankin-Selberg L-functions,
when level of both the associated forms vary in some range. Joint work with
Munshi and Singh. |
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| Date: | March 5, 2024 |
| Time: | 09:45am |
| Location: | BLOC 302 |
| Speaker: | Huimin Zhang, Shandong University |
| Title: | Hybrid subconvexity bounds for twists of GL_2 × GL_2 L-functions |
| Abstract: | Subconvexity problem is one of the central topics in analytic number theory. In this talk, we report on hybrid subconvexity bounds for GL_2 × GL_2 Rankin--Selberg L-functions twisted by a primitive Dirichlet character χ modulo a prime power, in the t and depth aspects. This is a joint work with Chenchen Shao. |
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| Date: | March 26, 2024 |
| Time: | 09:45am |
| Location: | BLOC 302 |
| Speaker: | Radu Toma, University of Bonn |
| Title: | The sup-norm problem for newforms in higher rank |
| Abstract: | I will present some new results on the sup-norm problem in the
level aspect for SL(n). The main novelties are in the geometry of numbers, where we develop a general reduction theory with level structure. Connected to it is an investigation of Atkin-Lehner operators in higher rank. The outcome is the first sub-baseline bound in the level aspect for the size of Hecke-Maass cuspidal newforms in unbounded rank. |
|
| Date: | April 9, 2024 |
| Time: | 09:45am |
| Location: | BLOC 302 |
| Speaker: | Zhining Wei, Brown University |
| Title: | Effective Open Image Theorem for pairs of elliptic curves |
| Abstract: | In 1972, Serre proved the celebrated Open Image Theorem, claiming that for a non-CM elliptic curve E over Q, the residue modulo $\ell$ Galois representation associated with E is surjective for sufficiently large prime $\ell$. An effective version of this theorem seeks to bound such least non-surjective prime $\ell$. In the talk, I will review some results concerning the effective version of Serre's Open Image Theorem. Then, I will present a work in progress on the effective open image theorem for pairs of elliptic curves, especially the semistable elliptic curves. This is joint with Tian Wang. |
|
| Date: | April 16, 2024 |
| Time: | 09:45am |
| Location: | BLOC 302 |
| Speaker: | Eun Hye Lee, Texas Christian University |
| Title: | Subconvexity of Shintani Zeta Functions |
| Abstract: | Subconvexity problem has been a central interest in analytic number theory for over a century. The strongest possible form of the subconvexity problem is the Lindelof hypothesis, which is a consequence of the RH, in the Riemann zeta function case. There have been many attempts to break convexity for diverse zeta and L functions, usually using the moments method. In this talk, I will introduce the Shintani zeta functions, and present another way to prove a subconvex bound. |
|
| Date: | April 23, 2024 |
| Time: | 09:45am |
| Location: | BLOC 302 |
| Speaker: | Shifan Zhao, The Ohio State University |
| Title: | Low-lying zeros of L-functions attached to Siegel modular forms |
| Abstract: | The Katz-Sarnak heuristic predicts that the distribution of low-lying zeros of families of automorphic L-functions are governed by certain classical compact groups determined by the family. In this talk I will present some recent progress concerning low-lying zeros of spinor and standard L-functions of Siegel modular forms. I will first describe these results in the $k$ (weight) aspect, and then explain how to extend the support of Fourier transforms of test functions by averaging over $k$. I will also discuss applications towards the non-vanishing of central L-values. |
|
| Date: | April 30, 2024 |
| Time: | 09:45am |
| Location: | BLOC 302 |
| Speaker: | Junxian Li, University of California, Davis |
| Title: | Joint value distribution of L-functions |
| Abstract: | I will discuss the joint value distribution of L- functions in the critical strip. The values of distinct primitive L-functions behave like independently distributed random variables on the critical line, but some dependence shows up away from the critical line. Nevertheless, we can show distinct L-functions can obtain large/small values simultaneously infinitely often. Based on joint work with S. Inoue and W. Heap. |
|
| Date: | May 6, 2024 |
| Time: | 11:00am |
| Location: | BLOC 302 |
| Speaker: | John Sung Min Lee, University of Illinois at Chicago |
| Title: | On the distribution in arithmetic progressions of primes of various properties related to elliptic curves |
| Abstract: | Given an elliptic curve $E/\mathbb{Q}$ and a prime $p$ of good reduction for $E$, let $\widetilde{E}_p(\mathbb{F}_p)$ denote the group of $\mathbb{F}_p$-rational points of the reduction of $E$ modulo $p$. One can define primes with various properties associated with $E$ based on the structure of $\widetilde{E}_p(\mathbb{F}_p)$. For instance, we call $p$ a prime of cyclic reduction, $m$-divisibility, and Koblitz reduction for $E$ if $\widetilde{E}_p(\mathbb{F}_p)$ is cyclic, has an order divisible by $m$, and has a prime order, respectively. In this talk, we study how the aforementioned primes, for an individual elliptic curve or on average, are distributed across arithmetic progressions. Furthermore, we analyze whether these primes are equally distributed or biased over congruence classes modulo $n$. This work is a partial collaboration with Nathan Jones, Jacob Mayle, and Tian Wang. |
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