BIMSA > BIMSA-YMSC Tsinghua Number Theory Seminar Uniform Non-vanishing of Hilbert Modular L-values
Uniform Non-vanishing of Hilbert Modular L-values
Organizers
Hansheng Diao , Heng Du , Yueke Hu , Bin Xu , Yihang Zhu
Speaker
Liyang Li
Time
Monday, December 23, 2024 10:00 AM - 11:00 AM
Venue
Shuangqing-C654
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.