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

Masato Wakayama, Keitaro Yamamoto

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)173-186
Number of pages14
JournalRamanujan Journal
Volume30
Issue number2
DOIs
Publication statusPublished - Jan 1 2013

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Elliptic function
Algebraic Differential Equations
Nonlinear Differential Equations
Weierstrass Function
Q-series
Eisenstein Series
Modular Group
Ramanujan
Rational function
Coefficient
Family

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Non-linear algebraic differential equations satisfied by a certain family of elliptic functions. / Wakayama, Masato; Yamamoto, Keitaro.

In: Ramanujan Journal, Vol. 30, No. 2, 01.01.2013, p. 173-186.

Research output: Contribution to journalArticle

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