山大数论讨论班

星期三，15:00-16:00，2025年春季学期（3 月开始）

中心校区明德楼 C704

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）

• 2025-03-19，Hui Wang 王慧  (山东大学)

  题目：A zero-density estimate for $L$-functions associated with $\rm GL(3)$ Hecke--Maass cusp forms and its application

  摘要：The zero-distribution problem of $L$-functions occupies a central role in analytic number theory as it is intimately connected with various problems involving primes, such as the distribution of primes in short intervals, gaps between primes, and so on. In this talk, we establish an asymptotic formula for the twisted second moment of $L$-functions associated with Hecke--Maass cusp forms $\phi$ for $\rm SL(3, \mathbb{Z})$, and further deduce a weighted zero-density estimate for these $L$-functions in the spectral aspect. As an application, we obtain an asymptotic formula for the moments of the function $S_\phi(t)=\pi^{-1}\arg L(1/2+it, \phi)$ without assuming the Generalized Riemann Hypothesis (GRH). Previously, such a formula was only known to hold under the GRH. This is a joint work with Professor Qingfeng Sun.

  地点：明德楼 C704

• 2025-03-21，周五， Jing-song Chai   柴劲松   (安徽工程大学)

  题目：Two applications of Bessel functions

  摘要：In this talk, we present two applications of Bessel functions. The first one is to use Bessel functions over finite field to study Asai gamma factors of GL(n). We also obtain a distinction criterion. The second is to use Bessel functions over p-adic field to obtain another Kirillov model for supercuspidal representations.

  地点：明德楼 C704

• 2025-04-02， Didier Lesesvre   (Université de Lille)

  题目：Kuznetsov trace formula for GSp(4) and applications

  摘要：Trace formulas relate statistics on automorphic forms, which often remain mysterious yet central in number theory, with statistics on geometric or arithmetic quantities, which one hopes to be more explicit and better understood. We will discuss how to establish such a Kuznetsov-type trace formula in the case of the symplectic group GSp(4), and will study the precise analytic behaviour of both the spectral and the arithmetic transforms arising in the formula. These fundamental properties can be used to establish various results on the family of Maaß automorphic forms on GSp(4) in the spectral aspect: the Weyl law, a density result on the non-tempered spectrum, large sieve inequalities, bounds on the second moment of the spinor and standard L-functions, as well as a statement on the distribution of the low-lying zeros of these L-functions.

  地点：明德楼 C704

• 2025-04-07，周一， Jun Yu   余君   (北京大学)    10:00-11:00

  题目： Positivity of Fourier transform of zonal spherical functions

  摘要： Given a semisimple real linear group, a zonal spherical function is matrix coefficient associated to the unique spherical vector with value 1 at identity element in a unitary spherical principal series, which are important object in representation theory and harminic analysis. Each zonal spherical function is a positive function. Hence, its Fourier transform along a maximal split torus is everywhere non-negative by a classical theorem of Bochner. In this talk we report a result in a recent joint work: the Fourier transform along a maximal split torus of any zonal spherical function takes positive value everywhere.

  地点：明德楼 C704

• 2025-04-09，  Shigeru Kanemitsu

  题目： Fourier-Whittaker expansion and the Epstein-type zeta-functions

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  地点： 洪家楼校区1号楼

• 2025-04-16，  Rui Zhang   张蕊   (山东大学)

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  地点： 明德楼 C704

• 2025-04-23，  

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• 2025-05-07，  Hengfei Lü 吕恒飞

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• 2025-05-14，  

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• 2025-05-28，  Lingmin Liao 廖灵敏

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• 2025-06-04，   

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• 2025-06-11，  

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• 2025-06-18，  

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往年报告：

• 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