Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	赵世帆，Ohio State University
Inviter:	王标
Title:	Siegel Zeros and Applications
Language:	Chinese
Time & Venue:	2023.01.11 09:00-10:00 Zoom ID: 841 4547 6856 Password: 1728
Abstract:	Siegel zeros are real zeros of L-functions that are very close to 1, the non-existence of which was conjectured as a direct consequence of the Grand Riemann Hypothesis (GRH). In this talk, we will start with Siegel zeros of Dirichlet L-functions - its origin, application and significance. We will then introduce Siegel zeros of general L-functions. In particular, we will talk about known cases of their non-existence, starting from the work of Hoffstein, Goldfeld and Lieman in 1994. Finally, I will talk about a recent result about the non-existence of Siegel zeros of certain symmetric power L-functions, and its application to lower bounds of those L-functions at s=1.