On signs of Fourier coefficients on GL(n)

2025/07/30 by Lesesvre, Didier, Ng, Ming Ho, Wang, Yingnan
#11F30 #11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.22718

Abstract

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.

Citations

• Weyl's law in the theory of automorphic forms

Related

• On Signs of Fourier Coefficients of Hecke-Maass Cusp Forms on GL₃
• Fourier coefficients of GL(N) automorphic forms in arithmetic progressions
• Fourier expansions of GL(2) newforms at various cusps
• Convoluted Fourier Coefficients of GL(n)-Automorphic Functions. Part 1
• Fourier coefficients for automorphic forms on quasisplit classical groups