Analytic properties of euler products of automorphic representations

1977 ◽  
pp. 11-26 ◽  
Author(s):  
C. J. Moreno
Keyword(s):  
Automorphic Representations ◽  
Euler Products

Effective Estimates for the Distribution of Values of Euler Products

2005 ◽  
Vol 145 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Ernesto Girondo ◽  
Jörn Steuding
Keyword(s):  
Distribution Of Values ◽  
Euler Products

scholarly journals CUSP FORMS ON GSp(4) WITH SO(4)-PERIODS

2011 ◽  
Vol 07 (04) ◽  
pp. 855-919
Author(s):  
YUVAL Z. FLICKER
Keyword(s):  
Quadratic Extension ◽  
Summation Formula ◽  
Unipotent Radical ◽  
Automorphic Representations ◽  
Orbital Integrals ◽  
Relative Trace Formula ◽  
Almost Everywhere ◽  
Genus 2 ◽  
Technical Advances ◽  
Ramanujan Conjecture

The Saito–Kurokawa lifting of automorphic representations from PGL(2) to the projective symplectic group of similitudes PGSp(4) of genus 2 is studied using the Fourier summation formula (an instance of the "relative trace formula"), thus characterizing the image as the representations with a nonzero period for the special orthogonal group SO(4, E/F) associated to a quadratic extension E of the global base field F, and a nonzero Fourier coefficient for a generic character of the unipotent radical of the Siegel parabolic subgroup. The image is nongeneric and almost everywhere nontempered, violating a naive generalization of the Ramanujan conjecture. Technical advances here concern the development of the summation formula and matching of relative orbital integrals.

Analytic behavior of some Euler products

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Jinho Han ◽  
Haseo Ki ◽  
Donghoon Park
Keyword(s):  
Analytic Behavior ◽  
Euler Products

scholarly journals Ramanujan identities and Euler products for a type of Dirichlet series

2006 ◽  
Vol 122 (4) ◽  
pp. 349-393 ◽  
Author(s):  
Zhi-Hong Sun ◽  
Kenneth S. Williams
Keyword(s):  
Dirichlet Series ◽  
Euler Products

scholarly journals Eisenstein Series Arising from Jordan Algebras

2019 ◽  
Vol 72 (1) ◽  
pp. 183-201 ◽  
Author(s):  
Marcela Hanzer ◽  
Gordan Savin
Keyword(s):  
Eisenstein Series ◽  
Jordan Algebra ◽  
Jordan Algebras ◽  
Algebra Structure ◽  
Parabolic Subgroups ◽  
Automorphic Representations ◽  
Unipotent Radicals ◽  
Maximal Parabolic Subgroups

AbstractWe describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.

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