Jacobi forms and generalized RC-algebras. (Q1414920)

Ten years ago \textit{D. Zagier} [Proc. Indian Acad. Sci., Math. Sci. 104, 57--75 (1994; Zbl 0806.11022)] introduced the so-called Rankin-Cohen algebras which consist of differential bilinear operators acting on the graded ring \(M(\Gamma)\) of modular forms with respect to some subgroup \(\Gamma\) of \(\text{PSL}_2 (\mathbb{Z})\). In the paper under review the authors continue their earlier work on Rankin-Cohen brackets with respect to Jacobi forms in the sense of Eichler-Zagier, where the heat operator is involved. In particular they study the algebraic properties of these generalized Rankin-Cohen algebras and give examples generalizing the elliptic case.