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).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
[Be] J. Bernstein’s Letter to I. Piatetski-Shapiro, Fall 1985.
[B,Z] I.N. Bernshtein and A.V. Zelevinskii,Representations of the group GL (n,F)where F is a non-archimedean local field, Russian Mathematical Surveys31 (1976), No. 3, 1–68.
[B,G] D. Bump and D. Ginzburg,Spin L-functions on symplectic groups, Duke Mathematical Journal68 (1992), 153–160.
[E,H] D. Eisenbud and J. Harris,Schemes: The Language of Modern Algebraic Geometry, Wadsworth & Brooks/Cole Mathematics Series, Pacific Grove, California, 1992, p. 13.
[G,PS] S. Gelbart and I. Piatetski-Shapiro,L-Functions for G×GL(n), inExplicit Constructions, of Automorphic L-Functions (S. Gelbart, I. Piatetski-Shapiro and S. Rallis, eds.), Lecture Notes in Mathematics1254, Springer-Verlag, Berlin, 1980.
[H] R. Hartshorne,Algebraic Geometry, Graduate Text in Mathematics52, Springer-Verlag, Berlin, 1977.
[Ho] R. Howe,Harish-Chandra homomorphisms for p-adic groups, Regional Conference Series in Mathematics59, Conference Board of the Mathematical Sciences, American Mathematical Society, 1985.
[J,PS,S] H. Jacquet, I. Piatetski-Shapiro and J. Shalika,Automorphic forms on GL(3)II, Annals of Mathematics109 (1979), 213–258.
[J,S.1] H. Jacquet and J. Shalika,Rankin-Selberg convolutions: archimedean theory, in Israel Mathematical Conference Proceedings, Festschrift in honor of Ilya Piatetski-Shapiro, Part I (S. Gelbart, R. Howe and P. Sarnak, eds.), Weizmann Science Press of Israel, Jerusalem, 1990.
[J,S.2] H. Jacquet and J. Shalika,Exterior square L-functions, inAutomorphic Forms, Shimura Varieties and L-functions (L. Clozel and J. Milne, eds.), Vol. II, Proceedings of a Conference held at the University of Michigan, Ann Arbor, July 1988.
[S] D. Soudry,Rankin-Selberg convolutions for SO2l+1×GLn:Local theory, Memoris of the American Mathematical Society105 (No. 500) (1993), 1–100.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vo, S.C. The spinL-function on the symplectic groupGSp(6). Isr. J. Math. 101, 1–71 (1997). https://doi.org/10.1007/BF02760921
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02760921