Spin $\mathrm {L}$-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
DOI:
https://doi.org/10.1090/S0002-9947-99-02174-1
Published electronically:
July 7, 1999
MathSciNet review:
1473433
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The βspinβ 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.
- Avner Ash, David Ginzburg, and Steven Rallis, Vanishing periods of cusp forms over modular symbols, Math. Ann. 296 (1993), no. 4, 709β723. MR 1233493, DOI https://doi.org/10.1007/BF01445131
- Michel Brion, Invariants dβun sous-groupe unipotent maximal dβun groupe semi-simple, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 1, 1β27 (French). MR 698847
- Daniel Bump and David Ginzburg, Spin $L$-functions on symplectic groups, Internat. Math. Res. Notices 8 (1992), 153β160. MR 1177328, DOI https://doi.org/10.1155/S1073792892000175
- W. Casselman and J. Shalika, The unramified principal series of $p$-adic groups. II. The Whittaker function, Compositio Math. 41 (1980), no. 2, 207β231. MR 581582
- David Ginzburg, On spin $L$-functions for orthogonal groups, Duke Math. J. 77 (1995), no. 3, 753β798. MR 1324640, DOI https://doi.org/10.1215/S0012-7094-95-07723-0
- David Ginzburg, On standard $L$-functions for $E_6$ and $E_7$, J. Reine Angew. Math. 465 (1995), 101β131. MR 1344132, DOI https://doi.org/10.1515/crll.1995.465.101
- Tamotsu Ikeda, On the location of poles of the triple $L$-functions, Compositio Math. 83 (1992), no. 2, 187β237. MR 1174424
- Dihua Jiang, Degree $16$ standard $L$-function of ${\rm GSp}(2)\times {\rm GSp}(2)$, Mem. Amer. Math. Soc. 123 (1996), no. 588, viii+196. MR 1342020, DOI https://doi.org/10.1090/memo/0588
- HervΓ© Jacquet and Joseph Shalika, Exterior square $L$-functions, Automorphic forms, Shimura varieties, and $L$-functions, Vol. II (Ann Arbor, MI, 1988) Perspect. Math., vol. 11, Academic Press, Boston, MA, 1990, pp. 143β226. MR 1044830
- Stephen S. Kudla and Stephen Rallis, A regularized Siegel-Weil formula: the first term identity, Ann. of Math. (2) 140 (1994), no. 1, 1β80. MR 1289491, DOI https://doi.org/10.2307/2118540
- David Soudry, Rankin-Selberg convolutions for ${\rm SO}_{2l+1}\times {\rm GL}_n$: local theory, Mem. Amer. Math. Soc. 105 (1993), no. 500, vi+100. MR 1169228, DOI https://doi.org/10.1090/memo/0500
- San Cao Vo, The spin $L$-function on the symplectic group ${\rm GSp}(6)$, Israel J. Math. 101 (1997), 1β71. MR 1484868, DOI https://doi.org/10.1007/BF02760921
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
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
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
