Institution: | Department of Mathematics, RKM Vivekananda College, Mylapore, Chennai 600 004, India B. Ramakrishnan ; Mehta Research Institute of Mathematics and Mathematical Physics, Chhatnag Rd., Jhusi, Allahabad 211 019, India |
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. |