• Corpus ID: 120247210

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

  title={Abel's Theorem and the Allied Theory: Including the Theory of the Theta Functions},
  author={Henry Frederick Baker},
  • H. Baker
  • Published 17 October 2007
  • Mathematics
Multi-dimensional sigma-functions
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
Cubic theta functions
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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
Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models
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
On Jacobi Inversion Formulae for Telescopic Curves
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
On the superintegrable Richelot systems
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
Schottky vertex operator cluster algebras
  • A. Zuevsky
  • Mathematics
    International Journal of Modern Physics A
  • 2022
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
New generalisation of Jacobi’s derivative formula
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