Growth of Fourier coefficients of vector-valued automorphic forms

TL;DR

This paper proves polynomial bounds on the growth of Fourier coefficients for vector-valued automorphic forms of certain groups, and discusses their L-functions and exponential sums.

Contribution

It establishes polynomial-growth bounds for Fourier coefficients of vector-valued automorphic forms, extending understanding of their analytic properties.

Findings

Fourier coefficients grow at most polynomially

L-functions associated with these forms are analyzed

Exponential sums related to the forms are discussed

Abstract

In this article, we establish polynomial-growth bound for the sequence of Fourier coefficients associated to even integer weight vector-valued automorphic forms of Fuchsian groups of the first kind. At the end, their $L$-functions and exponential sums have been discussed.