Abelian functions associated with genus three algebraic curves

Abstract

We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and an advancement of efficient symbolic computation techniques has 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.

arXiv comment34 pages

References in corpus (7)

• Abelian Functions for Cyclic Trigonal Curves of Genus Four
• Abelian functions associated with a cyclic tetragonal curve of genus six
• Identities for hyperelliptic P-functions of genus one, two and three in covariant form
• Sigma, tau and Abelian functions of algebraic curves
• On Hyperelliptic Abelian Functions of Genus 3
• A genus six cyclic tetragonal reduction of the Benney equations
• Some addition formulae for Abelian functions for elliptic and hyperelliptic curves of cyclotomic type

Cited by in corpus (4)

• Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion
• On the equivariant algebraic Jacobian for curves of genus two
• Abelian function fields on Jacobian varieties
• Some New Addition Formulae for Weierstrass Elliptic Functions