On some estimates involving Fourier coefficients of Maass cusp forms

Author:

Sun Qingfeng1,Wang Hui2

Affiliation:

1. School of Mathematics and Statistics, Shandong University, Weihai, Weihai, Shandong 264209, P. R. China

2. School of Mathematics, Shandong University, Jinan 250100, P. R. China

Abstract

Let [Formula: see text] be a Hecke–Maass cusp form for [Formula: see text] with Laplace eigenvalue [Formula: see text] and let [Formula: see text] be its [Formula: see text]th normalized Fourier coefficient. It is proved that, uniformly in [Formula: see text], [Formula: see text] where the implied constant depends only on [Formula: see text]. We also consider the summation function of [Formula: see text] and under the Ramanujan conjecture we are able to prove [Formula: see text] with the implied constant depending only on [Formula: see text].

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

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