On the size of p-adic Whittaker functions

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.

41 pages, v4: Minor corrections, including suggestions by the anonymous Referee. Accepted for publication by the Transactions of the American Mathematical Society

References in corpus (3)

• Hybrid sup-norm bounds for Maass newforms of powerful level
• On the order of vanishing of newforms at cusps
• Large values of newforms on GL(2) with highly ramified central character

Cited by in corpus (5)

• On sup-norm bounds part II: $GL(2)$ Eisenstein series
• Sup norms of newforms on $G{L}_2$ with highly ramified central character
• Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity
• Adelic Voronoi Summation and Subconvexity for GL(2) L-Functions in the depth Aspect
• The sup-norm problem beyond the newform