Averages of long Dirichlet polynomials with modular coefficients
Number Theory
2023-06-29 v2
Abstract
We study the moments of -functions associated with primitive cusp forms, in the weight aspect. In particular, we obtain an asymptotic formula for the twisted moments of a \textit{long} Dirichlet polynomial with modular coefficients. 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.
Cite
@article{arxiv.2207.12989,
title = {Averages of long Dirichlet polynomials with modular coefficients},
author = {Brian Conrey and Alessandro Fazzari},
journal= {arXiv preprint arXiv:2207.12989},
year = {2023}
}