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Corpus ID: 120247210

Abel's Theorem and the Allied Theory: Including the Theory of the Theta Functions

@inproceedings{Baker2007AbelsTA,
title={Abel's Theorem and the Allied Theory: Including the Theory of the Theta Functions},
author={Henry Frederick Baker},
year={2007}
}

In 1997 the present authors published a review (Ref. BEL97 in the present manuscript) that recapitulated and developed classical theory of Abelian functions realized in terms of multi-dimensional… Expand

We compare and contrast three different methods for the construction of the differential relations satisfied by the fundamental Abelian functions associated with an algebraic curve. We realize these… Expand

The main purpose of this paper is to extend results, which have been obtained previously to describe the classical scattering of solitons with integrable defects of type I, to include the much larger… Expand

For a hyperelliptic curve of genus $g$, it is well known that the symmetric products of $g$ points on the curve are expressed in terms of their Abel-Jacobi image by the hyperelliptic sigma function… Expand

We introduce the Richelot class of superintegrable systems in N-dimensions whose n ⩽ N equations of motion coincide with the Abel equations on the n − 1 genus hyperelliptic curve. Corresponding… Expand

Using recursion formulas for vertex operator algebra higher genus characters with formal parameters identified with local coordinates around marked points on a Riemann surface of arbitrary genus, we… Expand

A stream of new theta relations is obtained. They follow from general Thomae formula, which is a new result giving expressions for derivative theta constants (the lowest non-vanishing derivatives of… Expand