Uniform Non-vanishing of Hilbert Modular L-values

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker：

Liyang Yang (Princeton)

Time：

Monday, 10:00-11:00am

Dec. 23, 2024

Online：

Zoom Meeting ID: 4552601552

Passcode: YMSC

Title：

Uniform Non-vanishing of Hilbert Modular L-values

Abstract：

Let F(k,q) be the set of normalized Hilbert newforms of weight k and prime level q. In this talk, we will use a regularized relative trace formulas to establish a uniform positive proportion of #{\pi \in F(k,q) : L(1/2, \pi) \neq 0} as #F(k,q) tends to infinity. Our result matches the best-known outcomes in both the level and weight aspects. This is joint work with Zhining Wei and Shifan Zhao. If time permits, we will introduce a simultaneous non-vanishing result via a symmetric spectral reciprocity.