On Shimura, Shintani and Eichler-Zagier correspondences

Manickam, M.; Ramakrishnan, B.

doi:10.1090/S0002-9947-00-02423-5

On Shimura, Shintani and Eichler-Zagier correspondences
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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.

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