Fourier coefficients of GL(N) automorphic forms in arithmetic progressions
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- 作者：Emmanuel Kowalski (1)
Guillaume Ricotta (2) - 关键词：Vorono? summation formula ; generalized Bessel transforms ; fourier coefficients of GL(N) Hecke–Maass cusp forms ; arithmetic progressions ; central limit theorem ; hyper ; kloosterman sums ; monodromy group ; sato–Tate equidistribution ; 11F11 ; 11F30 ; 11T23 ; 11L05 ; 60F05
- 刊名：Geometric And Functional Analysis
- 出版年：2014
- 出版时间：August 2014
- 年：2014
- 卷：24
- 期：4
- 页码：1229-1297
- 全文大小：703 KB
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Guillaume Ricotta (2)
1. ETH Zürich-DMATH, R?mistrasse 101, 8092, Zürich, Switzerland
2. Université Bordeaux 1, Institut de Mathématiques de Bordeaux, 351, cours de la Liberation, 33405, Talence Cedex, France - ISSN：1420-8970
文摘
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 \({N \geq 2}\) , satisfy a central limit theorem in a suitable range, generalizing the case N?=?2 treated by Fouvry et?al. (Commentarii Math Helvetici, 2014). Such universal Gaussian behaviour relies on a deep equidistribution result of products of hyper-Kloosterman sums.