English

Averages of long Dirichlet polynomials with modular coefficients

Number Theory 2023-06-29 v2

Abstract

We study the moments of LL-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.

Keywords

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}
}
R2 v1 2026-06-25T01:14:43.996Z