DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES

Title & Authors
DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES
Aygunes, Aykut Ahmet;

Abstract
In this paper, by using the modular forms of weight nk ($\small{2{\leq}n{\in}\mathbb{N}}$ and $\small{k{\in}\mathbb{Z}}$), 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. We also give some properties of an operator related to the derivative formula. Finally, by using the function $\small{j_4}$, we obtain the Fourier coefficients of modular forms with weight 4.
Keywords
Eisenstein series;modular forms;cusp forms;Fourier series;operators;derivative formula;theta function;Jacobi theta function;
Language
English
Cited by
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