We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and the advancement of efficient symbolic computation techniques have allowed for recent progress in this area. In this paper we focus on the genus three cases, comparing the two canonical classes of hyperelliptic and trigonal curves. We present new addition formulae, derive bases for the spaces of Abelian functions and discuss the differential equations such functions satisfy.
|Number of pages
|LMS Journal of Computation and Mathematics
|Published - 1 Dec 2011
- abelian functions
- genus 3