Quasimodular forms as solutions of Modular differential equations

Peter J. Grabner*

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

We study quasimodular forms of depth ≤ 4 and determine under which conditions they occur as solutions of modular differential equations. Furthermore, we study which modular differential equations have quasimodular solutions. We use these results to investigate extremal quasimodular forms as introduced by M. Kaneko and M. Koike further. Especially, we prove a conjecture stated by these authors concerning the divisors of the denominators occurring in their Fourier expansion.

Originalspracheenglisch
Seiten (von - bis)2233 - 2274
Seitenumfang42
FachzeitschriftInternational Journal of Number Theory
Jahrgang16
Ausgabenummer10
DOIs
PublikationsstatusVeröffentlicht - 1 Nov 2020

ASJC Scopus subject areas

  • !!Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

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