Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type
J. C. Eilbeck, S. Matsutani, and Y. Onishi
TL;DR
This paper derives new addition formulae for Abelian functions on specific elliptic and hyperelliptic curves with many automorphisms, expanding the mathematical toolkit for these special curves.
Contribution
It introduces novel addition formulae for Weierstrass functions on specialized genus one and two curves, including equianharmonic, lemniscate, and Burnside curves.
Findings
New addition formulae for equianharmonic and lemniscate elliptic curves
New addition formulae for certain genus two hyperelliptic curves
Enhanced understanding of automorphism-rich curves
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Coding theory and cryptography