Differential operators for Hermitian Jacobi forms and Hermitian modular forms

Congruences in Hermitian Jacobi and Hermitian modular forms

“…We assume that i t+1 = i 1 + (p − 1) for our convenience. By (16) and the third assertion of this Lemma, for each j with 1 ≤ j ≤ t, there exists an integer s ≥ 2 such that (18) Ω(L…”

“…We next recall Rankin-Cohen brackets of Hermitian modular forms which is a main ingredient in the proof of Proposition 7.7. Martin and Senadheera [18] have defined Rankin-Cohen brackets of two Hermitian modular forms. We need only the first Rankin-Cohen bracket of two Hermitian modular forms for our purpose.…”

Theta operator on Hermitian modular forms over the Eisenstein field

“…The theory of a theta operator on the Hermitian modular forms was developed by several researchers (e.g., [12], [8]). We recall that the Fourier expansion of the Hermitian modular form can be regarded as an element of the formal power series ring…”

“…The same type of statement in the case K = Q(i) was given in [8], Theorem 3. A similar method using the Rankin-Cohen bracket is applicable for the case K = Q( √ 3 i) (e.g., [12]). and p = 7.…”

“…The theory of a theta operator on the Hermitian modular forms was developed by several researchers (e.g., [12], [8]).…”