Abelian functions associated with genus three algebraic curves
J.C. Eilbeck, M. England, Y. Onishi
TL;DR
This paper advances the theory of Abelian functions for genus three algebraic curves, comparing hyperelliptic and trigonal cases, and introduces new addition formulas, bases, and differential equations for these functions.
Contribution
It provides new addition formulas, bases, and differential equations for Abelian functions associated with genus three algebraic curves, focusing on hyperelliptic and trigonal classes.
Findings
New addition formulas for genus three Abelian functions
Explicit bases for spaces of Abelian functions
Differential equations satisfied by these functions
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.
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