Spin L-functions on and

Authors:
Daniel Bump and David Ginzburg

Journal:
Trans. Amer. Math. Soc. **352** (2000), 875-899

MSC (1991):
Primary 11F66, 11F46; Secondary 11F70

DOI:
https://doi.org/10.1090/S0002-9947-99-02174-1

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 is an Euler product of degree associated with the spin representation of the L-group . If or , 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.

**[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 -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 -Functions for Orthogonal Groups*, Duke Math. J.**77**(1995), 753-798. MR**96f:11076****[G2]**D. Ginzburg,*On Standard -Functions for and*, J. Reine Angew. Math.**465**(1995), 101-131. MR**96m:11040****[I]**T. Ikeda,*On the Location of Poles of the Triple -Functions*, Comp. Math.**83**(1992). MR**94b:11042****[J]**D. Jiang,*Degree standard -function of*, Mem. Amer. Math. Soc.,**123**(1996), no. 588. MR**97d:11081****[J-S]**H. Jacquet and J. Shalika,*Exterior Square -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 : Local Theory*, Mem. Amer. Math. Soc.**500**(1994). MR**94b:11043****[V]**S. Vo,*The spin L-function on the symplectic group*, Israel Journal of Mathematics**101**(1997), 1-71. MR**98j:11038**

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Additional Information

**Daniel Bump**

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

Email:
bump@math.stanford.edu

**David Ginzburg**

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

Email:
ginzburg@math.tau.ac.il

DOI:
https://doi.org/10.1090/S0002-9947-99-02174-1

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