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arXiv · 1310.5223

Fourier coefficients of GL(N) automorphic forms in arithmetic progressions

Emmanuel Kowalski·Guillaume Ricotta
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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 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.

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Emmanuel Kowalski, Guillaume Ricotta. 2014-06-12. Fourier coefficients of GL(N) automorphic forms in arithmetic progressions. https://arxiv.org/abs/1310.5223

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