On strong multiplicity one for automorphic representations

2002/10/16 by C. S. Rajan, Rajan, C. S.
Mathematics · #11F70 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F70

paper · pdf · doi:10.48550/arxiv.math/0210235

8 pages

arxiv created 2002/10/16 · arxiv updated 2009/11/30

Abstract

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GL_n(\A_K). Let S be a set of finite places of K, such that the sum ∑_{v∈ S}Nv^-2/(n2+1) is convergent. Then π is uniquely determined by the collection of the local components \π_v| v\not∈ 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 solvable extensions of K, and where π is determined upto twisting by a character of the Galois group of L over K.

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