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Factorization of the local exterior square L-function of \(GL_m\)

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Abstract

Let \(\pi \) be an irreducible generic representation of \(GL_m(F)\), where F is a non-Archimedean local field. In 1990, Jacquet and Shalika established an integral representation of exterior square L-functions of \(GL_m(F)\). Following the works of Cogdell and Piatetski-Shapiro, we characterize exceptional poles in terms of certain Shalika functionals on the derivatives of \(\pi \), 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 \(\pi \).

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Acknowledgements

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.

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  1. Yeongseong Jo

    Present address: Department of Mathematics, The University of Iowa, Iowa City, IA, 52242, USA

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  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Yeongseong Jo

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Jo, Y. Factorization of the local exterior square L-function of \(GL_m\). manuscripta math. 162, 493–536 (2020). https://doi.org/10.1007/s00229-019-01140-x

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