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A multi-variable Rankin–Selberg integral for a product of \(GL_2\)-twisted Spinor L-functions

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Abstract

We consider a new integral representation for \(L(s_1, \Pi \times \tau _1) L(s_2, \Pi \times \tau _2),\) where \(\Pi \) is a globally generic cuspidal representation of \(GSp_4,\) and \(\tau _1\) and \(\tau _2\) are two cuspidal representations of \(GL_2\) having the same central character. As and application, we find a new period condition for two such L functions to have a pole simultaneously. This points to an intriguing connection between a Fourier coefficient of a residual representation on GSO(12) and a theta function on Sp(16). A similar integral on GSO(18) fails to unfold completely, but in a way that provides further evidence of a connection.

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Authors and Affiliations

  1. Department of Mathematics, 244 Mathematics Building, University at Buffalo, Buffalo, NY, 14260-2900, USA

    Joseph Hundley

  2. Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George St., Room 6290, Toronto, ON, M5S 2E4, Canada

    Xin Shen

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  1. Joseph Hundley
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  2. Xin Shen
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Correspondence to Joseph Hundley.

Additional information

Communicated by J. Schoißengeier.

This paper was written while the first named author was supported by NSF Grant DMS-1001792.

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Hundley, J., Shen, X. A multi-variable Rankin–Selberg integral for a product of \(GL_2\)-twisted Spinor L-functions. Monatsh Math 181, 355–403 (2016). https://doi.org/10.1007/s00605-015-0868-7

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  • DOI: https://doi.org/10.1007/s00605-015-0868-7

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