Averages of long Dirichlet polynomials with modular coefficients
Speaker: Alessandro Fazzari
Date: Fri, Jul 29, 2022
Location: PIMS, University of Northern British Columbia
Conference: Moments of L-functions Workshop
Subject: Mathematics
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Date: Fri, Jul 29, 2022
Location: PIMS, University of Northern British Columbia
Conference: Moments of L-functions Workshop
Subject: Mathematics
Class: Scientific
CRG: L-Functions in Analytic Number Theory
Abstract:
We study the moments of $L$-functions associated with primitive cusp forms, in the weight aspect. In particular, we present recent joint work with Brian Conrey, where we obtain an asymptotic formula for the twisted $r$-th moment of a long Dirichlet polynomial approximation of such $L$-functions. This result, which is conditional on the Generalized Lindel\"of Hypothesis, agrees with the prediction of the recipe by Conrey, Farmer, Keating, Rubinstein and Snaith.
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