Addition formulae for Abelian functions associated with specialized curves

J. C. Eilbeck, S. Matsutani, Y. Ônishi

Research output: Contribution to journalArticle

Abstract

We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of low genus with many automorphisms, concentrating mostly on the case of genus 1 and 2. In the genus 1 case, we give addition formulae for the equianharmonic and lemniscate cases, and in genus 2 we find some new addition formulae for a number of curves. © 2011 The Royal Society.

Original languageEnglish
Pages (from-to)1245-1263
Number of pages19
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume369
Issue number1939
DOIs
Publication statusPublished - 28 Mar 2011

Fingerprint

Addition formula
Genus
Curve
Lemniscate of Bernoulli
Weierstrass Function
Automorphisms
Term

Keywords

  • Abelian functions
  • Addition formulae
  • Sigma functions
  • Weierstrass functions

Cite this

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Addition formulae for Abelian functions associated with specialized curves. / Eilbeck, J. C.; Matsutani, S.; Ônishi, Y.

In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 369, No. 1939, 28.03.2011, p. 1245-1263.

Research output: Contribution to journalArticle

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AU - Ônishi, Y.

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