Fourier coefficients of half-integral weight modular forms in arithmetic progressions
Year: 2019
Type: preprint
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 Salié sums.
Author: Darreye, Corentin
Institution: Institut de Mathématiques de Bordeaux
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4287867944