Number Theory Seminar

Date: March 27, 2019

Time: 1:45PM - 2:45PM

Location: BLOC 220

Speaker: Wei-Lun Tsai, Texas A&M University

Title: Arithmetic statistics of canonical Hecke L-functions

Abstract: The canonical Hecke characters in the sense of Rohrlich form a set of algebraic Hecke characters with important arithmetic properties. For example, the central values of their corresponding L-functions are related to ranks of Gross's elliptic Q-curves. In this talk, we explain how non-trivial bounds for l-torsion in class groups of number fields can be used to prove that for an asymptotic density of 100 percent of CM fields E within certain general families, the number of canonical Hecke characters of E whose L-function has a nonvanishing central value is >> |disc(E)|^{delta} for some absolute constant delta > 0. This is joint work with B. D. Kim and Riad Masri.

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