Poles of p-adic Asai L-functions and distinguished representations

TL;DR

This paper establishes a p-adic criterion linking Asai L-functions to distinguished automorphic representations over real quadratic fields, extending Flicker's theorem into the p-adic setting.

Contribution

It introduces a p-adic analogue of Flicker's theorem, connecting poles of p-adic Asai L-functions with distinguished representations.

Findings

Criterion for distinguished representations via p-adic Asai L-functions

Extension of Flicker's theorem to p-adic context

Characterization of poles of p-adic Asai L-functions

Abstract

We give a criterion in terms of p-adic Asai L-functions for a cuspidal automorphic representation of GL(2) over a real quadratic field to be a distinguished representation, providing a p-adic counterpart of a well-known theorem of Flicker for the complex Asai L-function.