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Cohen–Kuznetsov liftings of quasimodular forms

Volume 171 / 2015

Min Ho Lee Acta Arithmetica 171 (2015), 241-256 MSC: 11F11, 11F50. DOI: 10.4064/aa171-3-3

Abstract

Jacobi-like forms for a discrete subgroup $\varGamma $ of ${\rm SL}(2,\mathbb R)$ are formal power series which generalize Jacobi forms, and they correspond to certain sequences of modular forms for $\varGamma $. Given a modular form $f$, a Jacobi-like form can be constructed by using constant multiples of derivatives of $f$ as coefficients, which is known as the Cohen–Kuznetsov lifting of $f$. We extend Cohen–Kuznetsov liftings to quasimodular forms by determining an explicit formula for a Jacobi-like form associated to a quasimodular form.

Authors

  • Min Ho LeeDepartment of Mathematics
    University of Northern Iowa
    Cedar Falls, IA 50614, U.S.A.
    e-mail

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