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Uniform Non-vanishing of Hilbert Modular L-values

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

Liyang Li

时间

2024年12月23日 10:00 至 11:00

地点

Shuangqing-C654

摘要

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.