Fourier coefficients of GL(N) automorphic forms in arithmetic progressions
Number Theory
2014-06-13 v3 Algebraic Geometry
Abstract
We show that the multiple divisor functions of integers in invertible residue classes modulo a prime number, as well as the Fourier coefficients of GL(N) Maass cusp forms for all N larger than 2, satisfy a central limit theorem in a suitable range, generalizing the case N=2 treated by E. Fouvry, S. Ganguly, E. Kowalski and P. Michel. Such universal Gaussian behaviour relies on a deep equidistribution result of products of hyper-Kloosterman sums.
Cite
@article{arxiv.1310.5223,
title = {Fourier coefficients of GL(N) automorphic forms in arithmetic progressions},
author = {Emmanuel Kowalski and Guillaume Ricotta},
journal= {arXiv preprint arXiv:1310.5223},
year = {2014}
}