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


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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