The modular differential equation for skew-holomorphic Jacobi forms

Shotaro Kimura*

*この研究の対応する著者

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1137-1146
ページ数10
ジャーナルRamanujan Journal
59
4
DOI
出版ステータスPublished - 2022 12月

ASJC Scopus subject areas

  • 代数と数論

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