Cohen–Kuznetsov liftings of quasimodular forms

Min Ho Lee¹

¹ Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614, U.S.A.

Acta Arithmetica, Tome 171 (2015) no. 3, pp. 241-256

Résumé

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.

Détail

DOI : 10.4064/aa171-3-3

Keywords: jacobi like forms discrete subgroup vargamma mathbb formal power series which generalize jacobi forms correspond certain sequences modular forms vargamma given modular form jacobi like form constructed using constant multiples derivatives coefficients which known cohen kuznetsov lifting extend cohen kuznetsov liftings quasimodular forms determining explicit formula jacobi like form associated quasimodular form