DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES

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Aygunes A. A.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.52, no.2, pp.333-347, 2015 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 52 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.4134/jkms.2015.52.2.333
  • Journal Name: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.333-347
  • Keywords: Eisenstein series, modular forms, cusp forms, Fourier series, operators, derivative formula, theta function, Jacobi theta function, EISENSTEIN, SERIES
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: No

Abstract

In this paper, by using the modular forms of weight nk (2 <= n is an element of N and k is an element of 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.