Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Spin L-functions on $GSp_{8}$ and $GSp_{10}$

Authors: Daniel Bump and David Ginzburg
Journal: Trans. Amer. Math. Soc. 352 (2000), 875-899
MSC (1991): Primary 11F66, 11F46; Secondary 11F70
Published electronically: July 7, 1999
MathSciNet review: 1473433
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The ``spin'' L-function of an automorphic representation of $GSp_{2n}$ is an Euler product of degree $2^{n}$ associated with the spin representation of the L-group $\mathrm{GSpin}(2n+1)$. If $n=4$ or $5$, and the automorphic representation is generic in the sense of having a Whittaker model, the analytic properties of these L-functions are studied by the Rankin-Selberg method.

References [Enhancements On Off] (What's this?)

  • [A-G-R] A. Ash, D. Ginzburg and S. Rallis, Vanishing periods of cusp forms over modular symbols, Math. Ann. 296 (1993). MR 94f:11044
  • [B] M. Brion, Invariants d'un sous-groupe unipotent maximal d'un groupe semi-simple, Ann. Inst. Fourier, Grenoble 33 (1983), 1-27. MR 85a:14031
  • [B-G] D. Bump and D. Ginzburg, Spin $L$-Functions on Symplectic Groups, Internat. Math. Res. Notices 8 (1992), 153-160. MR 93i:11060
  • [C-S] W. Casselman and J. Shalika, The Unramified Principal Series of p-adic Groups II: the Whittaker Function, Comp. Math. 41 (1980), 207-231. MR 83i:22027
  • [G1] D. Ginzburg, On Spin $L$-Functions for Orthogonal Groups, Duke Math. J. 77 (1995), 753-798. MR 96f:11076
  • [G2] D. Ginzburg, On Standard $L$-Functions for $E_{6}$ and $E_{7}$, J. Reine Angew. Math. 465 (1995), 101-131. MR 96m:11040
  • [I] T. Ikeda, On the Location of Poles of the Triple $L$-Functions, Comp. Math. 83 (1992). MR 94b:11042
  • [J] D. Jiang, Degree $16$ standard $L$-function of $GSp(2)\times GSp(2)$, Mem. Amer. Math. Soc., 123 (1996), no. 588. MR 97d:11081
  • [J-S] H. Jacquet and J. Shalika, Exterior Square $L$-Functions, in Automorphic Forms, Shimura Variaties and L-Functions, L. Clozel and J. S. Milne ed., Vol. 2 (1990), 143-226. MR 91g:11050
  • [K-R] S. Kudla and S. Rallis, A Regularized Siegel-Weil Formula: the First Term Identity, Annals of Math. 140 (1994), 1-80. MR 95f:11036
  • [S] D. Soudry, Rankin-Selberg Convolutions for $SO_{2\ell +1}\times GL_{n}$: Local Theory, Mem. Amer. Math. Soc. 500 (1994). MR 94b:11043
  • [V] S. Vo, The spin L-function on the symplectic group $GSp(6)$, Israel Journal of Mathematics 101 (1997), 1-71. MR 98j:11038

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 11F66, 11F46, 11F70

Retrieve articles in all journals with MSC (1991): 11F66, 11F46, 11F70

Additional Information

Daniel Bump
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305

David Ginzburg
Affiliation: School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Keywords: Spin L-functions
Received by editor(s): January 7, 1997
Received by editor(s) in revised form: May 26, 1997
Published electronically: July 7, 1999
Additional Notes: This work was supported in part by NSF Grant DMS-9622819.
Article copyright: © Copyright 1999 American Mathematical Society