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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Shimura, Shintani and Eichler-Zagier correspondences


Authors: M. Manickam and B. Ramakrishnan
Journal: Trans. Amer. Math. Soc. 352 (2000), 2601-2617
MSC (2000): Primary 11F11, 11F37, 11F50; Secondary 11F25, 11F30
Published electronically: March 7, 2000
MathSciNet review: 1637086
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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.


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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
Email: ramki@mri.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02423-5
PII: S 0002-9947(00)02423-5
Keywords: Jacobi forms, modular forms of half-integral weight, newforms
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
Article copyright: © Copyright 2000 American Mathematical Society