DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES
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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. We also give some properties of an operator related to the derivative formula. Finally, by using the function j4, we obtain the Fourier coefficients of modular forms with weight 4.
Abstract
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. We also give some properties of an operator related to the derivative formula. Finally, by using the function j4, we obtain the Fourier coefficients of modular forms with weight 4.
참고문헌 (7)
- T. M. Apostol, "Modular functions and Dirichlet series in Number Theory" (1976), Springer-Verlag
- A. A. Aygunes, "A formula for generating modular forms with weight 4", ~
- A. A. Aygunes, "Hecke Operators Related to the Generalized Dedekind Eta Functions and Applications", Numer. Anal. Appl. Math, 1-3, pp.1098~1101 (2010)
- A. A. Aygunes, "A sequence of modular forms associated with higher order derivative Weierstrass-type functions", ~
- E. Hecke, "Mathematische Werke" (1983), Vandenhoeck & Ruprecht in G¨ottingen
- A. Hurwitz, "Ueber die Differentialgleichungen dritter Ordnung, welchen die Formen mit linearen Transformationen in sich gen¨u gen", Math. Ann, 33(3), pp.345~352 (1889)
- L. J. P. Kilford, "Modular Forms: a classical and computational introduction" (2008), Imperial College Press