On the size of p-adic Whittaker functions

TL;DR

This paper establishes precise bounds for p-adic Whittaker functions associated with GL(2) representations over non-archimedean fields using the p-adic stationary phase method.

Contribution

It provides the first comprehensive bounds for Whittaker new vectors in all cases, advancing understanding of their size in non-archimedean representation theory.

Findings

Derived explicit bounds for Whittaker functions

Applied p-adic stationary phase technique effectively

Unified treatment across all representation types

Abstract

In this paper we tackle a question raised by N. Templier and A. Saha concerning the size of Whittaker new vectors appearing in infinite dimensional representations of GL(2) over non-archimedean fields. We derive precise bounds for such functions in all possible situations. Our main tool is the p-adic method of stationary phase.