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arXiv · 1810.10424

Quadratic forms connected with Fourier coefficients of holomorphic and Maass cusp forms

Giamila Zaghloul
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Abstract

In this work we prove a prime number type theorem involving the normalised Fourier coefficients of holomorphic and Maass cusp forms, using the classical circle method. A key point is in a recent paper of Fouvry and Ganguly, based on Hoffstein-Ramakrishnan's result about the non-existence of the Siegel zeros for $GL(2)$ $L$-functions, which allows us to improve preceding estimates.

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Giamila Zaghloul. 2018-10-24. Quadratic forms connected with Fourier coefficients of holomorphic and Maass cusp forms. https://doi.org/10.1016/j.jnt.2016.03.018

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