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

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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.

Original language	English
Pages (from-to)	173-186
Number of pages	14
Journal	Ramanujan Journal
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s11139-012-9425-3
Publication status	Published - Feb 2013

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-012-9425-3

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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",

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AB - 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.

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

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