Jacobi forms and the heat operator. II
[For Part I, cf. Math. Z. 225, 95-101 (1997; Zbl 0869.11045).] Classically, there are many connections between differential operators and the theory of elliptic modular forms and many interesting results have been explored. Recently, many theorems about Jacobi forms have been studied. It turns out that Jacobi forms play important roles in the theory of numbers. Jacobi forms are connected with modular forms of half-integral weight as well as integral weight, Siegel forms and elliptic curves. The heat operator plays an important role in connecting Jacobi forms and elliptic modular forms. Recently, the bilinear differential operators, called Rankin-Cohen type bracket operators, on Jacobi forms have been defined using the heat operator by the author. In this paper, he shows how to construct more Jacobi forms using the heat-operator. Originally, Eicher-Zagier have shown how to construct modular forms from Jacobi forms. The author's main result is a generalization of the result given by Eichler-Zagier to Jacobi forms. He also studies further examples.
scientific article; zbMATH DE number 1191156