title: Addition formulae for Abelian functions associated with specialized curves.
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.
authors.affiliation: Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK. j.c.eilbeck@hw.ac.uk
authors.forename: J C
authors.initials: JC
authors.lastname: Eilbeck
authors.forename: S
authors.initials: S
authors.lastname: Matsutani
authors.forename: Y
authors.initials: Y
authors.lastname: Onishi
mesh_terms: D017711:Nonlinear Dynamics; D011789:Quantum Theory