Quasimodular forms as solutions of Modular differential equations

Peter J. Grabner

doi:10.1142/S1793042120501158

Quasimodular forms as solutions of Modular differential equations

Peter J. Grabner^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2233 - 2274
Number of pages	42
Journal	International Journal of Number Theory
Volume	16
Issue number	10
DOIs	https://doi.org/10.1142/S1793042120501158
Publication status	Published - 1 Nov 2020

Keywords

math.NT
11F11 34A05
modular differential equations
Balanced quasimodular forms
quasimodular vectors
extremal quasimodular forms

ASJC Scopus subject areas

Algebra and Number Theory

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1142/S1793042120501158

https://arxiv.org/abs/2002.02736

Cite this

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AB - 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.

KW - math.NT

KW - 11F11 34A05

KW - modular differential equations

KW - Balanced quasimodular forms

KW - quasimodular vectors

KW - extremal quasimodular forms

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ER -

Quasimodular forms as solutions of Modular differential equations

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

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