Non-linear algebraic differential equations satisfied by a certain family of elliptic functions

Masato Wakayama; Keitaro Yamamoto

doi:10.1007/s11139-012-9425-3

Non-linear algebraic differential equations satisfied by a certain family of elliptic functions

Masato Wakayama, Keitaro Yamamoto

総長・役員等

研究成果: Contribution to journal › Article › 査読

抄録

Kurokawa and Wakayama (Ramanujan J. 10:23-41, 2005) studied a family of elliptic functions defined by certain q-series. This family, in particular, contains the Weierstrass ℘-function. In this paper, we prove that elliptic functions in this family satisfy certain non-linear algebraic differential equations whose coefficients are essentially given by rational functions of the first few Eisenstein series of the modular group.

本文言語	英語
ページ（範囲）	173-186
ページ数	14
ジャーナル	Ramanujan Journal
巻	30
号	2
DOI	https://doi.org/10.1007/s11139-012-9425-3
出版ステータス	出版済み - 2 2013

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

文献へのアクセス

10.1007/s11139-012-9425-3

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引用スタイル

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abstract = "Kurokawa and Wakayama (Ramanujan J. 10:23-41, 2005) studied a family of elliptic functions defined by certain q-series. This family, in particular, contains the Weierstrass ℘-function. In this paper, we prove that elliptic functions in this family satisfy certain non-linear algebraic differential equations whose coefficients are essentially given by rational functions of the first few Eisenstein series of the modular group.",

author = "Masato Wakayama and Keitaro Yamamoto",

note = "Funding Information: M. Wakayama{\textquoteright}s work is in part supported by Grant-in-Aid for Scientific Research (B) No. 21340011.",

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