Joint value distribution of $L$-functions

Abstract: It is believed that distinct primitive $L$-functions are “statistically independent”. The independence can be interpreted in many different ways. We are interested in the joint value distributions and their applications in moments and extreme values for distinct $L$-functions. We discuss some large deviation estimates in Selberg and Bombieri-Hejhal’s central limit theorem for values of several $L$-functions. On the critical line, values of distinct primitive $L$-functions behave independently in a strong sense. However, away from the critical line, values of distinct Dirichlet $L$-functions begin to exhibit some correlations.

This is based on joint works with Shota Inoue.

Mathematics

Audience: researchers in the topic

CRG Weekly Seminars

Series comments: These seminars will be centered on various topics in L-functions in analytic number theory. If you are interested, please register here to receive the Zoom link: uleth.zoom.us/meeting/register/tJ0ucO-spjkvEtGdqQv0rwzSYNjWjYBohVTu