Factorization of the local exterior square L-function of GLm

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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
Issue number3-4
StatePublished - 1 Jul 2020

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


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