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The spinL-function on the symplectic groupGSp(6)

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Abstract

In this paper, we will study some essential analytic properties of the “spin”L-function on the symplectic groupGSp (6) (which is associated with the eight-dimensional spin representation of theL-group Gspin (7, ℂ), namely, uniqueness of a bilinear form on an irreducible admissible representation ofGSp (6)×GL(2), local functional equation, and meromorphic continuation, non-vanishing properties at non-archimedean places as well as at archimedean places.

Consequently, we will determine the location of the possible poles of the global spinL-function of a generic automorphic cuspidal representation ofGSp(6).

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    San Cao Vo

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  1. San Cao Vo
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Correspondence to San Cao Vo.

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Vo, S.C. The spinL-function on the symplectic groupGSp(6). Isr. J. Math. 101, 1–71 (1997). https://doi.org/10.1007/BF02760921

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  • DOI: https://doi.org/10.1007/BF02760921

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