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3 results

  • QUASIMODULAR FORMS AND COHOMOLOGY

  • Part of
  • Min Ho Lee
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 86 / Issue 1 / August 2012
    Published online by Cambridge University Press:
    15 December 2011, pp. 150-163
    Print publication:
    August 2012
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  • We construct linear maps from the spaces of quasimodular forms for a discrete subgroup Γ of SL(2,ℝ) to some cohomology spaces of the group Γ and prove that these maps are equivariant with respect to appropriate Hecke operator actions. The results are obtained by using the fact that there is a correspondence between quasimodular forms and certain finite sequences of modular forms.

  • HEAT OPERATORS AND QUASIMODULAR FORMS

  • Part of
  • MIN HO LEE
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 81 / Issue 3 / June 2010
    Published online by Cambridge University Press:
    28 January 2010, pp. 514-522
    Print publication:
    June 2010
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  • We introduce a differential operator on quasimodular polynomials that corresponds to the derivative operator on quasimodular forms. We then prove that such a differential operator is compatible with a heat operator on Jacobi-like forms in certain cases. These results show in those cases that the derivative operator on quasimodular forms corresponds to a heat operator on Jacobi-like forms.

  • QUASIMODULAR FORMS AND VECTOR BUNDLES

  • Part of
  • MIN HO LEE
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 80 / Issue 3 / December 2009
    Published online by Cambridge University Press:
    02 July 2009, pp. 402-412
    Print publication:
    December 2009
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  • Modular forms for a discrete subgroup Γ of SL(2,ℝ) can be identified with holomorphic sections of line bundles over the modular curve U corresponding to Γ, and quasimodular forms generalize modular forms. We construct vector bundles over U whose sections can be identified with quasimodular forms for Γ.