scholarly journals On strong multiplicity one for automorphic representations

2003 ◽  
Vol 102 (1) ◽  
pp. 183-190 ◽  
Author(s):  
C.S. Rajan
Keyword(s):  
Automorphic Representations ◽  
Multiplicity One ◽  
Strong Multiplicity

scholarly journals Unitary dual of GL(n) at archimedean places and global Jacquet–Langlands correspondence

2010 ◽  
Vol 146 (5) ◽  
pp. 1115-1164 ◽  
Author(s):  
A. I. Badulescu ◽  
D. Renard
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Automorphic Representations ◽  
Langlands Correspondence ◽  
General Linear Groups ◽  
Multiplicity One ◽  
Unitary Dual ◽  
Strong Multiplicity ◽  
Local Results

AbstractIn a paper by Badulescu [Global Jacquet–Langlands correspondence, multiplicity one and classification of automorphic representations, Invent. Math. 172 (2008), 383–438], results on the global Jacquet–Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field were established, under the assumption that the local inner forms are split at archimedean places. In this paper, we extend the main local results of that article to archimedean places so that the above condition can be removed. Along the way, we collect several results about the unitary dual of general linear groups over ℝ, ℂ or ℍ which are of independent interest.

scholarly journals A conjectural refinement of strong multiplicity one for GL(n)

2021 ◽  
pp. 1-16
Author(s):  
Nahid Walji
Keyword(s):  
Number Field ◽  
Lower Bounds ◽  
Automorphic Representations ◽  
Hecke Eigenvalues ◽  
Multiplicity One ◽  
Strong Multiplicity ◽  
Cuspidal Automorphic Representations

Given a pair of distinct unitary cuspidal automorphic representations for GL([Formula: see text]) over a number field, let [Formula: see text] denote the set of finite places at which the automorphic representations are unramified and their associated Hecke eigenvalues differ. In this paper, we demonstrate how conjectures on the automorphy and possible cuspidality of adjoint lifts and Rankin–Selberg products imply lower bounds on the size of [Formula: see text]. We also obtain further results for GL(3).

Strong multiplicity one for Siegel cusp forms of degree two

2021 ◽  
Vol 33 (5) ◽  
pp. 1157-1167
Author(s):  
Arvind Kumar ◽  
Jaban Meher ◽  
Karam Deo Shankhadhar
Keyword(s):  
Symplectic Group ◽  
Cusp Forms ◽  
Multiplicity One ◽  
Strong Multiplicity

Abstract We prove strong multiplicity one results for Siegel eigenforms of degree two for the symplectic group Sp 4 ⁡ ( ℤ ) {\operatorname{Sp}_{4}(\mathbb{Z})} .

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