Differential Operators on Jacobi Forms of Several Variables

Differential operators on Hermitian Jacobi forms

“…P r o o f. The proof is analogues to that given in [4]. LetJ k,m be the set of formal power series expansion of the form in (3.1) satisfying the equation (3.5).…”

On Rankin-Cohen brackets for Siegel modular forms

“…3) Choie and Kim [5] also determine multilinear operators on J k, M (Γ 1 ). One can use their result to construct multilinear operators on Siegel modular forms of degree n. This allows one to generalize the main result in Choie [3] to the case where n > 2.…”

“…We denote the vector space of such Jacobi forms by J k, M (Γ 1 ). Choie and Kim [5] provide an explicit formula for the Rankin-Cohen bracket for Jacobi forms on J k, M (Γ 1 ). We need the following definition to state their main result.…”

“…Explicit formulas for Rankin-Cohen brackets have been found for Jacobi forms ( [1] and [2]), Siegel modular forms of degree 2 ([3] and [4]), and for Jacobi forms (of higher degree) on H × C n ( [5]). Eholzer and Ibukiyama [7] prove that there exists a unique Rankin-Cohen bracket for Siegel modular forms of arbitrary degree n. A closed formula for the Rankin-Cohen bracket is known only for n = 1 and 2, even though a system of recursion relations is given for any degree n in [7].…”

Differential operators on Hilbert modular forms

“…Rankin-Cohen brackets have been studied for elliptic modular forms, Jacobi forms, and Siegel modular forms. For more details, see [1][2][3][4][5]10,19].…”