Fourier coefficients of GL(N) automorphic forms in arithmetic progressions |
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Authors: | Emmanuel Kowalski Guillaume Ricotta |
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Institution: | 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
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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 \({N \geq 2}\) , 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. |
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