On signs of Fourier coefficients on GL(n)

Fuente: arXiv
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Main Authors: Lesesvre, Didier, Ng, Ming Ho, Wang, Yingnan
Format: Preprint
Published: 2025
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author Lesesvre, Didier
Ng, Ming Ho
Wang, Yingnan
author_facet Lesesvre, Didier
Ng, Ming Ho
Wang, Yingnan
contents We study statistical properties of Fourier coefficients of automorphic forms on GL(n). For most Hecke-Maass cusp forms, we give the asymptotic number of nonvanishing coefficients, show that there is a positive proportion of sign changes among them, when these are real, and describe the asymptotic density of these signs. We generalize the results by Jääsaari obtained in the case of self-dual forms of GL(3) and our method moreover circumvents the assumption of the Generalized Ramanujan Conjecture.
format Preprint
id arxiv_https___arxiv_org_abs_2507_22718
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On signs of Fourier coefficients on GL(n)
Lesesvre, Didier
Ng, Ming Ho
Wang, Yingnan
Number Theory
11F30, 11N37
We study statistical properties of Fourier coefficients of automorphic forms on GL(n). For most Hecke-Maass cusp forms, we give the asymptotic number of nonvanishing coefficients, show that there is a positive proportion of sign changes among them, when these are real, and describe the asymptotic density of these signs. We generalize the results by Jääsaari obtained in the case of self-dual forms of GL(3) and our method moreover circumvents the assumption of the Generalized Ramanujan Conjecture.
title On signs of Fourier coefficients on GL(n)
topic Number Theory
11F30, 11N37
url https://arxiv.org/abs/2507.22718