On strong multiplicity one for automorphic representations

Rajan, C. S. (2003) On strong multiplicity one for automorphic representations Journal of Number Theory, 102 (1). pp. 183-190. ISSN 0022-314X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00223...

Related URL: http://dx.doi.org/10.1016/S0022-314X(03)00066-0

Abstract

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GLn(AK). Let S be a set of finite places of K, such that the sum ∑v∈SNv-2/(n2+1) is convergent. Then π is uniquely determined by the collection of the local components {πv|v∉S,v finite} of π . Combining this theorem with base change, it is possible to consider sets S of positive density, having appropriate splitting behavior with respect to a solvable extension L of K, and where π is determined up to twisting by a character of the Galois group of L over K.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Automorphic Representations; Strong Multiplicity One; Base Change
ID Code:38327
Deposited On:29 Apr 2011 11:29
Last Modified:17 May 2016 21:13

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