Fourier coefficients of automorphic $L$-functions over primes in ray classes

TL;DR

This paper establishes Siegel-Walfisz type theorems for Fourier coefficients of automorphic and Rankin-Selberg L-functions over primes in number fields, extending classical results to more general automorphic contexts.

Contribution

It proves new uniform distribution results for Fourier coefficients of automorphic L-functions over primes in ray classes in number fields.

Findings

Proved Siegel-Walfisz type theorems for automorphic L-functions.

Extended distribution results to short and long intervals.

Applied to primes in ray classes in number fields.

Abstract

We prove Siegel-Walfisz type theorems (over long and short intervals) for the Fourier coefficients of certain automorphic $L$-functions and Rankin-Selberg $L$-functions over number fields.