Fourier coefficients of half-integral weight modular forms in arithmetic progressions
Number Theory
2020-06-26 v4
Abstract
We study the probabilistic behavior of sums of Fourier coefficients in arithmetic progressions. We prove a result analogous to previous work of Fouvry-Ganguly-Kowalski-Michel and Kowalski-Ricotta in the context of half-integral weight holomorphic cusp forms and for prime power modulus. We actually show that these sums follow in a suitable range a mixed Gaussian distribution which comes from the asymptotic mixed distribution of Sali\'e sums.
Cite
@article{arxiv.1907.07483,
title = {Fourier coefficients of half-integral weight modular forms in arithmetic progressions},
author = {Corentin Darreye},
journal= {arXiv preprint arXiv:1907.07483},
year = {2020}
}