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Spinor $ L$-functions for generic cusp forms on $ GSp(2)$ belonging to principal series representations

Author(s): Taku Ishii; Tomonori Moriyama
Journal: Trans. Amer. Math. Soc. 360 (2008), 5683-5709.
MSC (2000): Primary 11F70; Secondary 11F41, 11F46.
Posted: June 19, 2008
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Abstract: Let $ \mathsf{G}=GSp(2)$ be the symplectic group with similitude of degree two, which is defined over $ \mathbf{Q}$. For a generic cusp form $ F$ on the adelized group $ \mathsf{G}_{\mathbf{A}}$ whose archimedean type is a principal series representation, we show that its spinor $ L$-function is continued to an entire function and satisfies the functional equation.

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Additional Information:

Taku Ishii
Affiliation: Department of Mathematics, Chiba Institute of Technology, 2-1-1 Shibazono, Narashino, Chiba, 275-0023, Japan
Email: ishii.taku@it-chiba.ac.jp

Tomonori Moriyama
Affiliation: Department of Mathematics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo, 102-8554 Japan
Address at time of publication: Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama-cho 1-1, Toyonaka, Osaka, 560-0043, Japan
Email: moriyama@mm.sophia.ac.jp, moriyama@math.sci.osaka-u.ac.jp

DOI: 10.1090/S0002-9947-08-04724-7
PII: S 0002-9947(08)04724-7
Keywords: Spinor $L$-functions, Novodvorsky's zeta integrals, Whittaker functions, principal series
Received by editor(s): June 15, 2005
Posted: June 19, 2008
Additional Notes: The first author was supported by JSPS Research Fellowships for Young Scientists.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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