山大数论讨论班

星期三，15:00-16:00，2025年秋季学期

中心校区明德楼 C704 & 洪家楼校区

组织者：山大数论组

讨论班着重于数论中的新进展。报告人为校内外学者和学生。欢迎推荐报告。

报告信息（摘要和往年报告信息见列表下方）

• 2025-09-17，杨一帆   台湾大学

  题目：

  摘要：

  地点：洪家楼校区1号楼

• 2025-09-24，杨一帆   台湾大学

  题目：

  摘要：

  地点：洪家楼校区

• 2025-10-29，华晟昊

  题目：Distribution of automorphic forms and families of $L$-functions

  摘要：Berry suggested that the eigenfunctions of chaotic systems can be modeled as random waves. It is widely believed that the moments of a normalized eigenfunction should coincide with those of a Gaussian distribution. In this talk, we will discuss a conjecture concerning the statistical independence in the joint distribution of Hecke--Maass cusp forms, along with two conditional results, based on joint work with Bingrong Huang and Liangxun Li.

  In one case, our proof relies on a phenomenon in which the moments of a ``mixed'' family of $L$-functions can be compared with those of a ``pure'' family of $L$-functions. This naturally raises the question: what constitutes a general family of $L$-functions?

  In the second part of the talk, I will introduce the toroidal families introduced by Fouvry, Kowalski, and Michel, which are defined via subgroups of characters. In ongoing joint work with Michel, we have developed a fundamental matrix framework that facilitates computations in the general setting. We illustrate this framework through examples spanning various ranks, including both low- and high-rank cases.

  地点：明德楼 C704

• 2025-12-15，程创勋   南京大学

  题目：On the splitting fields of principal homogeneous spaces for elliptic curves

  摘要：Let K/Qp be a finite extension and E/K be an elliptic curve. For a principal homogenous space C of E/K, the period of C is defined as the order of C as an element in the Weil-Châtelet group WC(E/K). A finite extension L/K is called a splitting field of C if C(L) is nonempty. It is known that when E/K has good reduction and the period of C is coprime to p, the extension L/K splits C if and only if the period of C divides the ramification index eL/K. The case in which the period of C is a power of p is more subtle. In this talk, I will present our recent work on this question for elliptic curves over Qp with good supersingular reduction and the period-index distribution problem.

  地点：明德楼 C704

• 2025-12-17，彭云剑   清华大学

  题目：Rankin--Selberg $L$-函数的 Weyl 界

  摘要：随着Rankin--Selberg $L$-函数的亚凸界问题已基本得到解决，Weyl界的研究成为该领域新的核心目标。本报告将介绍 Weyl 界的若干近期研究进展，并阐述我们借助相对迹公式与 adelic Voronoi求和公式，在一类新型Weyl界估计方面取得成果。

  地点：明德楼 C704

• 2025-12-24，叶李源   清华大学

  题目：Stationary phase analysis for analytic newvectors and applications to the subconvexity problem

  摘要：In this talk, I will discuss an extension of the results of Michel-Venkatesh and Hu-Michel-Nelson, establishing an upper bound for triple product and Rankin-Selberg L-functions of the form
  $$L(\pi_1\otimes\pi_2\otimes\pi_3,\frac{1}{2})\ll_{\pi_3,\epsilon}C(\pi_1\otimes\pi_2)^{\frac{1}{2}+\epsilon}\left(\frac{C(\pi_1\otimes\pi_2)}{C(\pi_2\otimes\pi_2)}\right)^{-\delta}$$
  in the spectral aspect, allowing conductor dropping. In particular, we obtain a subconvexity bound when $\pi_1\otimes\pi_2$  stays uniformly away from QUE-like case.

  地点：明德楼 C704

往年报告：

• 2025年春季报告
  

• 2024年秋季报告    2024年春季报告   
  

• 2023年秋季报告    2023年春季报告

• 2022年秋季报告 2022年春季报告

• 2021年秋季报告 2021年春季报告

• 2020年秋季报告 2020年春季报告

Contact us at: brhuang "at" sdu dot edu dot cn,   Office: Mingde C701,   Tel: 883-69786