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DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES
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논문 기본 정보

Type
Academic journal
Author
Journal
대한수학회 대한수학회지 대한수학회지 제52권 제2호 KCI Accredited Journals
Published
2015.1
Pages
333 - 347 (15page)

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DERIVATIVE FORMULAE FOR MODULAR FORMS AND THEIR PROPERTIES
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Abstract· Keywords

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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.
#Eisenstein series #modular forms #cusp forms #Fourier series #operators #derivative formula #theta function #Jacobi theta function

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References (7)

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T. M. Apostol / 1976 / Modular functions and Dirichlet series in Number Theory / Springer-Verlag google schola A. A. Aygunes / A formula for generating modular forms with weight 4 dbpia A. A. Aygunes / 2010 / Hecke Operators Related to the Generalized Dedekind Eta Functions and Applications / Numer. Anal. Appl. Math 1-3:1098~1101 google schola A. A. Aygunes / A sequence of modular forms associated with higher order derivative Weierstrass-type functions google schola E. Hecke / 1983 / Mathematische Werke / Vandenhoeck & Ruprecht in G¨ottingen google schola

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