Faculty Publications

Quasimodular Forms And Jacobi-Like Forms

Document Type

Article

Keywords

Jacobi-like forms, Modular forms, Quasimodular forms

Journal/Book/Conference Title

Mathematische Zeitschrift

Volume

280

Issue

3-4

First Page

643

Last Page

667

Abstract

We study various properties of quasimodular forms by using their connections with Jacobi-like forms. Such connections are made by identifying quasimodular forms for a discrete subgroup Γ of SL(2,ℝ) with certain polynomials over the ring of holomorphic functions of the Poincaré upper half plane that are Γ-invariant. We consider a surjective map from Jacobi-like forms to quasimodular forms and prove that it has a right inverse, which may be regarded as a lifting from quasimodular forms to Jacobi-like forms.

Department

Department of Mathematics

Original Publication Date

8-26-2015

DOI of published version

10.1007/s00209-015-1441-8

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