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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

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Spinor $L$-functions for generic cusp forms on $GSp(2)$ belonging to principal series representations
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by Taku Ishii and Tomonori Moriyama PDF
Trans. Amer. Math. Soc. 360 (2008), 5683-5709 Request permission

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
  • 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