Some results on archimedean Rankin–Selberg integrals

Jingsong Chai

Vol. 273 (2015), No. 2, 277–305

DOI: 10.2140/pjm.2015.273.277

Abstract

We use a notion of derivatives of smooth representations of moderate growth of $GL\left(n,ℝ\right)$ and exceptional poles to study local Rankin–Selberg integrals. We obtain various results which are archimedean analogs of $p$-adic results obtained by Cogdell and Piatetski-Shapiro.

Keywords

archimedean derivatives, exceptional poles, Rankin–Selberg integrals

Mathematical Subject Classification 2010

Primary: 11F70

Secondary: 22E46

Milestones

Received: 21 October 2013

Revised: 31 October 2013

Accepted: 4 November 2013

Published: 23 December 2014