Spinor $L$-functions for generic cusp forms on $GSp(2)$ belonging to principal series representations
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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.References
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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
- MR Author ID: 695361
- 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
- Received by editor(s): June 15, 2005
- Published electronically: June 19, 2008
- Additional Notes: The first author was supported by JSPS Research Fellowships for Young Scientists.
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 5683-5709
- MSC (2000): Primary 11F70; Secondary 11F41, 11F46
- DOI: https://doi.org/10.1090/S0002-9947-08-04724-7
- MathSciNet review: 2425688