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

Keywords

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

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