Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type

Abstract

We discuss a family of multi-term addition formulae for Weierstrass functions on specialized curves of genus one and two with many automorphisms. In the genus one case we find new addition formulae for the equianharmonic and lemniscate cases, and in genus two we find some new addition formulae for a number of curves, including the Burnside curve.

19 pages. We have extended the Introduction, corrected some typos and tidied up some proofs, and inserted extra material on genus 3 curves

References in corpus (5)

• Abelian Functions for Cyclic Trigonal Curves of Genus Four
• Abelian Functions for Trigonal Curves of Genus Three
• The Classification of Exceptional CDQL Webs on Compact Complex Surfaces
• On Algebraic Expressions of Sigma Functions for (n,s) Curves
• Spectral Curves of Operators with Elliptic Coefficients

Cited by in corpus (7)

• The Classification of Exceptional CDQL Webs on Compact Complex Surfaces
• Abelian functions associated with genus three algebraic curves
• Deriving bases for Abelian functions
• Thomae's Derivative Formulae for Trigonal Curves
• Some New Addition Formulae for Weierstrass Elliptic Functions
• The sigma function over a family of cyclic trigonal curves with a singular fiber
• A Recipe For Obtaining Algebraic Addition Theorems Of The Weierstrass Elliptic Function