scholarly journals On the Distribution of Hecke Eigenvalues for Cuspidal Automorphic Representations for GL(2)

2017 ◽  
pp. rnw331
Author(s):  
Nahid Walji
Keyword(s):  
Automorphic Representations ◽  
Hecke Eigenvalues ◽  
Cuspidal Automorphic Representations

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).

scholarly journals Galois representations attached to automorphic forms on over fields

2014 ◽  
Vol 150 (4) ◽  
pp. 523-567 ◽  
Author(s):  
Chung Pang Mok
Keyword(s):  
Automorphic Forms ◽  
Galois Representations ◽  
Suitable Condition ◽  
Two Dimensional ◽  
Automorphic Representations ◽  
Cuspidal Automorphic Representations ◽  
Central Characters

AbstractIn this paper we generalize the work of Harris–Soudry–Taylor and construct the compatible systems of two-dimensional Galois representations attached to cuspidal automorphic representations of cohomological type on ${\rm GL}_2$ over a CM field with a suitable condition on their central characters. We also prove a local-global compatibility statement, up to semi-simplification.

Poles ofL-functions and theta liftings for orthogonal groups

2009 ◽  
Vol 8 (4) ◽  
pp. 693-741 ◽  
Author(s):  
David Ginzburg ◽  
Dihua Jiang ◽  
David Soudry
Keyword(s):  
Eisenstein Series ◽  
Orthogonal Group ◽  
Symplectic Groups ◽  
Orthogonal Groups ◽  
Metaplectic Groups ◽  
Automorphic Representations ◽  
Domain Of Holomorphy ◽  
First Occurrence ◽  
Cuspidal Automorphic Representations

AbstractIn this paper, we prove that the first occurrence of global theta liftings from any orthogonal group to either symplectic groups or metaplectic groups can be characterized completely in terms of the location of poles of certain Eisenstein series. This extends the work of Kudla and Rallis and the work of Moeglin to all orthogonal groups. As applications, we obtain results about basic structures of cuspidal automorphic representations and the domain of holomorphy of twisted standardL-functions.

scholarly journals On the image of complex conjugation in certain Galois representations

2016 ◽  
Vol 152 (7) ◽  
pp. 1476-1488 ◽  
Author(s):  
Ana Caraiani ◽  
Bao V. Le Hung
Keyword(s):  
Symmetric Spaces ◽  
Galois Representations ◽  
Real Field ◽  
Complex Conjugation ◽  
Automorphic Representations ◽  
Locally Symmetric Spaces ◽  
Cuspidal Automorphic Representations ◽  
Totally Real ◽  
Totally Real Field

We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for $\text{GL}_{n}$ over a totally real field $F$.

scholarly journals Galois representations associated to holomorphic limits of discrete series

2013 ◽  
Vol 150 (2) ◽  
pp. 191-228 ◽  
Author(s):  
Wushi Goldring ◽  
Sug Woo Shin
Keyword(s):  
Galois Representations ◽  
Discrete Series ◽  
Unitary Groups ◽  
Main Ingredient ◽  
Automorphic Representations ◽  
Archimedean Component ◽  
Cuspidal Automorphic Representations

AbstractGeneralizing previous results of Deligne–Serre and Taylor, Galois representations are attached to cuspidal automorphic representations of unitary groups whose Archimedean component is a holomorphic limit of discrete series. The main ingredient is a construction of congruences, using the Hasse invariant, that is independent of$q$-expansions.

Integral Representation for U3 × GL2

2009 ◽  
Vol 61 (6) ◽  
pp. 1383-1406
Author(s):  
Eric Wambach
Keyword(s):  
Integral Representation ◽  
Unitary Group ◽  
Integral Representations ◽  
Automorphic Representations ◽  
Residual Spectrum ◽  
Cuspidal Automorphic Representations ◽  
Split Rank

Abstract Gelbart and Piatetskii-Shapiro constructed various integral representations of Rankin–Selberg type for groups G×GLn, where G is of split rank n. Here we show that their method can equally well be applied to the product U3 × GL2, where U3 denotes the quasisplit unitary group in three variables. As an application, we describe which cuspidal automorphic representations of U3 occur in the Siegel induced residual spectrum of the quasisplit U4.

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