Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES

  • Received : 2014.02.14
  • Published : 2015.03.01
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Abstract

In this paper, by using the modular forms of weight nk ($2{\leq}n{\in}\mathbb{N}$ and $k{\in}\mathbb{Z}$), 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 $j_4$, we obtain the Fourier coefficients of modular forms with weight 4.

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References

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