English

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

Algebraic Geometry 2011-03-15 v2

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.

Keywords

Cite

@article{arxiv.0803.3899,
  title  = {Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type},
  author = {J. C. Eilbeck and S. Matsutani and Y. Onishi},
  journal= {arXiv preprint arXiv:0803.3899},
  year   = {2011}
}

Comments

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