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

Masato Wakayama, Keitaro Yamamoto

Research output: Contribution to journalArticlepeer-review

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 - Feb 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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