Selberg's central limit theorem for quadratic Dirichlet L-functions over function fields
Speaker: Allysa Lumley
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
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
Abstract:
In this talk, we will discuss the logarithm of the central value L(12,χD) in the symplectic family of Dirichlet L-functions associated with the hyperelliptic curve of genus g over a fixed finite field Fq in the limit as g→∞. Unconditionally, we show that the distribution of log|L(12,χD)| is asymptotically bounded above by the full Gaussian distribution of mean 12logdeg(D) and variance logdeg(D), and also log|L(12,χD)| is at least 94.27% Gaussian distributed. Assuming a mild condition on the distribution of the low-lying zeros in this family, we obtain the full Gaussian distribution.
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