On the sum of the twisted Fourier coefficients of Maass forms by M\"obius function

TL;DR

This paper investigates upper bounds for sums of Fourier coefficients of Maass forms over specific subsets of integers, providing insights into their distribution and magnitude.

Contribution

It introduces new upper bounds for sums of Fourier coefficients of Maass forms over particular integer subsets, advancing understanding of their behavior.

Findings

Established non-trivial upper bounds for sums of Fourier coefficients

Analyzed sums over subsets with specific properties

Enhanced understanding of Fourier coefficient distribution

Abstract

In this paper, we study non-trivial upper bounds for the sum $\sum \limits_{n \in S} |\lambda_f(n)|$ where $f$ is a normalized Maass eigencusp form for the full modular group, $\lambda_f(n)$ is the $n$th normalized Fourier coefficient of $f$ and $S$ is a proper subset of positive integers in $[1,x]$ with certain properties.