THE ADJOINTNESS OF THE MAPS BETWEEN THE SPACE OF JACOBI FORMS AND THE SPACE OF MODULAR FORMS

Abstract

M. Eichler and D. Zagier constructed a map from a space of Jacobi forms to a space of elliptic modular forms. On the other hand, T. Satoh constructed a map from a space of cusp forms to a space of Jacobi cusp forms. In this paper, we prove a conjecture of N. P. Skoruppa to the effect that these maps are, up to constant, adjoint with respect to the Petersson products.