Faculty Publications

Title

Modular polynomials and derivatives of quasimodular forms

Document Type

Article

Keywords

modular forms, modular polynomials, quasimodular forms, quasimodular polynomials

Journal/Book/Conference Title

Complex Variables and Elliptic Equations

Volume

58

Issue

1

First Page

135

Last Page

148

Abstract

Modular polynomials are polynomials whose coefficients are modular forms of certain type, and they are in one-to-one correspondence with quasimodular polynomials that are naturally associated to quasimodular forms. In addition to the formal derivative operator ∂X, there is a differential operator Dλ on quasimodular polynomials corresponding to the derivative operator on quasimodular forms. We construct linear maps of quasimodular polynomials corresponding to certain linear maps of modular polynomials and prove that such maps reduce to the operators Dλ and ∂X in special cases. © 2013 Copyright Taylor and Francis Group, LLC.

Original Publication Date

1-1-2013

DOI of published version

10.1080/17476933.2011.557156

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