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2 results

  • 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
    • Article
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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.

  • JACOBI-LIKE FORMS, PSEUDODIFFERENTIAL OPERATORS, AND GROUP COHOMOLOGY

  • Part of
  • MIN HO LEE
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 78 / Issue 1 / August 2008
    Published online by Cambridge University Press:
    01 August 2008, pp. 55-71
    Print publication:
    August 2008
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  • Pseudodifferential operators are formal Laurent series in the formal inverse ∂−1 of the derivative operator ∂ whose coefficients are holomorphic functions on the Poincaré upper half-plane. Given a discrete subgroup Γ of SL(2,ℝ), automorphic pseudodifferential operators for Γ are pseudodifferential operators that are Γ-invariant, and they are closely linked to Jacobi-like forms and modular forms for Γ. We construct linear maps from the space of automorphic pseudodifferential operators and from the space of Jacobi-like forms for Γ to the cohomology space of the group Γ, and prove that these maps are compatible with the respective Hecke operator actions.