Cohen–Kuznetsov liftings of quasimodular forms
Tom 171 / 2015
Acta Arithmetica 171 (2015), 241-256
MSC: 11F11, 11F50.
DOI: 10.4064/aa171-3-3
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.
