Growth of Fourier coefficients of vector-valued automorphic forms

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.

31 pages, article has been revised: a new section (Section 6) is added