A sequence of modular forms associated with higher-order derivatives of Weierstrass-type functions

Abstract

In this article, we first determine a sequence { f n (τ)} n∈N of modular forms with weight 2 n k + 4(2 n−1 − 1) (n ∈ N; k ∈ N \ {1}; N := {1, 2, 3, • • • }). We then present some applications of this sequence which are related to the Eisenstein series and the cusp forms. We also prove that higher-order derivatives of the Weierstrass type ℘ 2n-functions are related to the above-mentioned sequence { f n (τ)} n∈N of modular forms.

Derivative Formulae for Modular Forms and Their Properties

“…In this paper, by using the modular forms of weight nk (2 ≤ n ∈ N and k ∈ Z), we construct a formula which generates modular forms of weight 2nk + 4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms.…”