Faculty Publications

Differential Operators On Modular Forms Associated To Quasimodular Forms

Document Type

Article

Keywords

Jacobi-like forms, Modular forms, Quasimodular forms, Rankin–Cohen brackets, Theta series

Journal/Book/Conference Title

Ramanujan Journal

Volume

39

Issue

1

First Page

133

Last Page

147

Abstract

A quasimodular form ϕ of depth at most m corresponds to holomorphic functions (Formula presented.). Given nonnegative integers (Formula presented.) and (Formula presented.) with (Formula presented.), we introduce a linear differential operator (Formula presented.) of order (Formula presented.) on modular forms whose coefficients are given in terms of derivatives of the functions (Formula presented.). We then show that Rankin–Cohen brackets of modular forms can be expressed in terms of such operators. As an application, we obtain differential operators associated to certain theta series studied by Dong and Mason.

Department

Department of Mathematics

Original Publication Date

1-1-2016

DOI of published version

10.1007/s11139-014-9648-6

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

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