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

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

2008-03-27

arxiv.org/abs/0803.3899v2

Phil. Trans. Roy. Soc. A., 369, 1245--1263 (2011)

Mathematics

Algebraic Geometry

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

Scientific paper

10.1098/rsta.2010.0320

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.

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