Factorization of the local exterior square L-function of GLm

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Abstract

Let π be an irreducible generic representation of GLm(F) , where F is a non-Archimedean local field. In 1990, Jacquet and Shalika established an integral representation of exterior square L-functions of GLm(F). Following the works of Cogdell and Piatetski-Shapiro, we characterize exceptional poles in terms of certain Shalika functionals on the derivatives of π, where “derivatives” are in the sense of Bernstein and Zelevinsky. We prove the factorization of local L-functions, which was originally observed by Cogdell and Piatetski-Shapiro: local exterior square L-functions can be expressed in terms of exceptional L-functions of the derivatives of π.

Original languageEnglish
Pages (from-to)493-536
Number of pages44
JournalManuscripta Mathematica
Volume162
Issue number3-4
DOIs
StatePublished - 1 Jul 2020

Bibliographical note

Funding Information:
This research was partially supported by National Science Foundation (NSF) Grant DMS-0968505 through Professor Cogdell. This work is an extension of the study embarked by Cogdell and Piatetski-Shapiro [ 11 ]. The author would like to thank his advisor Professor James W. Cogdell for suggesting this project and many careful reading of several preliminary versions of this paper. The author also thanks Professor Nadir Matringe for notifying errors in his papers to him and giving useful comments. The author are very grateful to the referee for very detailed and valuable suggestions which improve the exposition of this paper. This manuscript is the part of the author’s Ph.D. dissertation.

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

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