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.
|Number of pages||19|
|Journal||Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 28 Mar 2011|
- Abelian functions
- Addition formulae
- Sigma functions
- Weierstrass functions