The modular differential equation for skew-holomorphic Jacobi forms

Shotaro Kimura*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the modular differential equation for skew-holomorphic Jacobi forms, which are non-holomorphic modular forms. This differential equation is a second-order linear ordinary differential equation and similar to the case of elliptic modular forms, whose studies were initiated by Kaneko and Zagier. On the other hand, this equation differs from the case of holomorphic Jacobi forms introduced by Kiyuna in the types of differential equations and dependences on the index. We show the same properties as previous studies: the solution space of the differential equation is modular invariant and the differential equation is unique.

Original languageEnglish
JournalRamanujan Journal
DOIs
Publication statusAccepted/In press - 2022
Externally publishedYes

Keywords

  • Differential operator
  • Kaneko–Zagier differential equation
  • Modular differential equation
  • Skew-holomorphic Jacobi forms

ASJC Scopus subject areas

  • Algebra and Number Theory

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