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

Giamila Zaghloul

doi:10.1016/j.jnt.2016.03.018

paper

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

arXiv:1810.10424 · doi:10.1016/j.jnt.2016.03.018

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 $G L (2)$ $L$ -functions, which allows us to improve preceding estimates.

10 pages