Shalika periods on GL₂(D) and GL₄

Hervé Jacquet and Kimball Martin

Vol. 233 (2007), No. 2, 341–370

DOI: 10.2140/pjm.2007.233.341

Abstract

The exterior square L-function attached to an automorphic cuspidal representation of GL_2n has a pole if and only if a certain period integral does not vanish on the space of the representation. We conjecture, in the “if” direction, a similar result is true for representations of GL₂(D), where D is a division algebra. We prove a partial result which provides evidence for the conjecture. The proof is based on a relative trace formula.

Keywords

exterior square L-function, trace formula

Mathematical Subject Classification 2000

Primary: 11F67

Secondary: 11F70, 11F72

Milestones

Received: 20 November 2006

Accepted: 8 May 2007

Published: 1 December 2007