Speaker: Min Lee, Lecturer, Royal Society University Research Fellow, University of Bristol

Date: December 14, 2022

Time: 20:00-21:00

Location: Zoom

Sponsor: School of Mathematics, Shandong University

Abstract:

The non-vanishing of L-series at the centre of the critical strip has long been a subject of great interest. An important example of the significance of non-vanishing is in the case of an L-series corresponding to a modular form of weight 2, where the non-vanishing at the central point has been shown to be equivalent to the finiteness of the group of rational points of the associated elliptic curve. In the case of higher rank L-functions whose Euler product has an even degree, such connections between non-vanishing at the central point and the finiteness of certain groups are believed to be true, but the relations remain purely conjectural. The symmetric cube L-series plays a role in one of these conjectures.

Ginzburg, Jiang and Rallis (2001) proved that the non-vanishing at the central point of the critical strip of the symmetric cube L-series of any GL(2) automorphic form is equivalent to the non-vanishing of a certain triple product integral. The main purpose of this talk is to use this equivalence to prove that there are in finitely many Maass-Hecke cuspforms over the imaginary quadratic field of discriminant -3 such that the central values of their symmetric cube L-functions do not vanish.

This is joint work with Jeff Hostein and Junehyuk Jung.

For more information, please visit:

http://www.math.sdu.edu.cn/info/1020/18099.htm