Archimedean zeta integrals for the exterior square L-functions on GLn

Bump and Friedberg introduced a zeta integral interpolating the standard and the exterior square L-functions on GLn simultaneously. We compute the (real) archimedean part of this zeta integral by using the explicit formulas of the principal series Whittaker functions on GLn(R) obtained by Oda and th...

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Bibliographic Details
Published inJournal of number theory Vol. 186; pp. 304 - 345
Main Author Ishii, Taku
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2018
Subjects
Archimedean zeta integrals
Automorphic L-functions on GL(n)
Principal series representations
Whittaker functions
Automorphic L-functions on GL(n)
Whittaker functions
11F70
Principal series representations
Archimedean zeta integrals
11F55
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Summary:Bump and Friedberg introduced a zeta integral interpolating the standard and the exterior square L-functions on GLn simultaneously. We compute the (real) archimedean part of this zeta integral by using the explicit formulas of the principal series Whittaker functions on GLn(R) obtained by Oda and the author. We show that the archimedean zeta integral coincides with the product of two archimedean L-factors.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2017.10.007