Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Acta Arithmetica / Wszystkie zeszyty

Streszczenie

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.