One-level density of zeros of Dirichlet L-functions over function fields

Speaker: Hua Lin

Date: Mon, Jul 25, 2022

Location: PIMS, University of Northern British Columbia

Conference: Moments of L-functions Workshop

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory


We compute the one-level density of zeros of order-$\ell$ Dirichlet $L$-functions over function fields $\mathbb{F}_q[t]$ for $\ell=3,4$ in the Kummer setting ($q\equiv1\pmod{\ell}$) and for $\ell=3,4,6$ in the non-Kummer setting ($q\not\equiv1\pmod{\ell}$). In each case, we obtain a main term predicted by Random Matrix Theory (RMT) and a lower order term not predicted by RMT. We also confirm the symmetry type of the family is unitary, supporting the Katz and Sarnak philosophy.

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