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Graduate Student Number Theory Learning Seminar

Pair Correlation for GL(2) L-functions

Kim Klinger-Logan (Rutgers)

Location:  zoom
Date & time: Tuesday, 26 January 2021 at 4:00PM - 5:00PM

Abstract: Montgomery (1972) first studied the pair correlation of the non-trivial zeros of the Riemann zeta function.  This work has been extended by Ozluk to examine the pair correlation of zeros of families of Dirichlet L-functions.  Examining certain families (as opposed to individual L-functions) yields better results in support of the Pair Correlation Conjecture.  In this talk, we will give a brief history of these results. We will then discuss recent work in collaboration with V. Chandee and X. Li extending similar results to a family GL(2) L-function. As with the case of Dirichlet L-functions, these pair correlation results give that, assuming GRH, in a certain sense, more than 93% of the zeros of Gamma_1(q) L-functions are simple.

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