Addition formulae for Abelian functions associated with specialized curves

作者：Eilbeck J C^*; Matsutani S; Onishi Y

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2011, 369(1939): 1245-1263.

DOI：10.1098/rsta.2010.0320

• Abelian functions
• sigma functions
• Weierstrass functions
• addition formulae

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.

• 出版日期2011-3-28