Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On Shimura, Shintani and Eichler-Zagier correspondences
HTML articles powered by AMS MathViewer

by M. Manickam and B. Ramakrishnan PDF
Trans. Amer. Math. Soc. 352 (2000), 2601-2617 Request permission

Abstract:

In this paper, we set up Shimura and Shintani correspondences between Jacobi forms and modular forms of integral weight for arbitrary level and character, and generalize the Eichler-Zagier isomorphism between Jacobi forms and modular forms of half-integral weight to higher levels. Using this together with the known results, we get a strong multiplicity 1 theorem in certain cases for both Jacobi cusp newforms and half-integral weight cusp newforms. As a consequence, we get, among other results, the explicit Waldspurger theorem.
References
Similar Articles
Additional Information
  • M. Manickam
  • Affiliation: Department of Mathematics, RKM Vivekananda College, Mylapore, Chennai 600 004, India
  • B. Ramakrishnan
  • Affiliation: Mehta Research Institute of Mathematics and Mathematical Physics, Chhatnag Rd., Jhusi, Allahabad 211 019, India
  • MR Author ID: 256629
  • Email: ramki@mri.ernet.in
  • Received by editor(s): November 5, 1997
  • Received by editor(s) in revised form: May 12, 1998, and July 14, 1998
  • Published electronically: March 7, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 2601-2617
  • MSC (2000): Primary 11F11, 11F37, 11F50; Secondary 11F25, 11F30
  • DOI: https://doi.org/10.1090/S0002-9947-00-02423-5
  • MathSciNet review: 1637086