Shalika periods on GL<sub>2</sub>(D) and GL<sub>4</sub>

Hervé Jacquet, Kimball Martin

Type: Article

Publication Date: 2007-12-01

Citations: 7

DOI: https://doi.org/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 GL 2 ( 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.

Locations

Pacific Journal of Mathematics - View - PDF

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Works Cited by This (19)

Action	Title	Year	Authors
+	The Geometry and Cohomology of Some Simple Shimura Varieties.	2001	Michael Harris Richard Taylor Vladimir G. Berkovich
+	Representations of GL(n) and division algebras over a p-adic field	1983	Jonathan David Rogawski
+	Automorphic forms and representations	1997	Daniel Bump
+ PDF Chat	On the Restriction to 𝒟* × 𝒟* of Representations of <i>p</i>-adic <i>GL</i><sub>2</sub>(𝒟)	2007	A. Raghuram
+	Kirillov theory for ${\rm GL}\sb 2(\mathscr {D})$ where $\mathscr {D}$ is a division algebra over a non-Archimedean local field	2000	Dipendra Prasad A. Raghuram
+	p-adicL-functions for GL(2n)	1994	Avner Ash David Ginzburg
+	The Multiplicity One Theorem for GL n	1974	J. A. Shalika
+	REPRESENTATIONS OF THE GROUP<i>GL</i>(<i>n</i>,<i>F</i>) WHERE<i>F</i>IS A NON-ARCHIMEDEAN LOCAL FIELD	1976	I. N. Bernshtein A. V. Zelevinskii
+	BASE CHANGE FOR GL(2)	1980	R. P. Langlands
+	Local Shalika models and functoriality	2008	Dihua Jiang Chufeng Nien Yujun Qin