Averages of long Dirichlet polynomials with modular coefficients

2022/07/26 by Conrey, Brian, Fazzari, Alessandro
#11F11 #11M99 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2207.12989

Abstract

We study the moments of L-functions associated with primitive cusp forms, in the weight aspect. In particular, we obtain an asymptotic formula for the twisted moments of a long Dirichlet polynomial with modular coefficients. This result, which is conditional on the Generalized Lindelöf Hypothesis, agrees with the prediction of the recipe by Conrey, Farmer, Keating, Rubinstein and Snaith.

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