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arXiv · 1907.07483

Fourier coefficients of half-integral weight modular forms in arithmetic progressions

Corentin Darreye
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Abstract

We study the probabilistic behavior of sums of Fourier coefficients in arithmetic progressions. We prove a result analogous to previous work of Fouvry-Ganguly-Kowalski-Michel and Kowalski-Ricotta in the context of half-integral weight holomorphic cusp forms and for prime power modulus. We actually show that these sums follow in a suitable range a mixed Gaussian distribution which comes from the asymptotic mixed distribution of Sali\'e sums.

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Corentin Darreye. 2019-07-17. Fourier coefficients of half-integral weight modular forms in arithmetic progressions. https://doi.org/10.1093/imrn

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