Functiones et Approximatio Commentarii Mathematici

Differential operators on modular forms associated to theta series

Min Ho Lee

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We construct an operator on modular forms by modifying the derivative operator using certain theta series. To show that the image of a~modular form under this operator is a~modular form we use Jacobi-like forms determined by theta series as well as quasimodular forms obtained from such Jacobi-like forms.

Article information

Funct. Approx. Comment. Math., Volume 52, Number 1 (2015), 75-82.

First available in Project Euclid: 20 March 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F50: Jacobi forms

modular forms theta series Jacobi-like forms quasimodular forms


Lee, Min Ho. Differential operators on modular forms associated to theta series. Funct. Approx. Comment. Math. 52 (2015), no. 1, 75--82. doi:10.7169/facm/2015.52.1.6.

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  • Y. Choie and M.H. Lee, Quasimodular forms, Jacobi-like forms, and pseudodifferential operators, preprint.
  • P.B. Cohen, Y. Manin, and D. Zagier, Automorphic pseudodifferential operators, Algebraic Aspects of Nonlinear Systems, Birkhäuser, Boston, 1997, pp. 17–47.
  • C. Dong and G. Mason, Transformation laws for theta functions, CRM Proc. Lecture Notes, vol. 30, Amer. Math. Soc., Providence, RI, 2001, pp. 15–26.
  • F. Martin and E. Royer, Formes modulaires et transcendance, Formes modulaires et périodes (S. Fischler, E. Gaudron, and S. Khémira, eds.), Soc. Math. de France, 2005, pp. 1–117.
  • B. Schoeneberg, Elliptic modular functions, Springer-Verlag, Heidelberg, 1974.
  • D. Zagier, Modular forms and differential operators, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 57–75.