## 12 Citations

Identities for hyperelliptic ℘-functions of genus one, two and three in covariant form

- Mathematics
- 2008

We give a covariant treatment of the quadratic differential identities satisfied by the ℘-functions on the Jacobian of smooth hyperelliptic curves of genus ⩽3.

Deriving Bases for Abelian Functions Matthew England

- Mathematics
- 2011

We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the…

Sigma, tau and Abelian functions of algebraic curves

- Mathematics
- 2010

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…

Abelian functions associated with a cyclic tetragonal curve of genus six

- Mathematics
- 2009

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y4 = x5 + λ4x4 + λ3x3 + λ2x2 + λ1x + λ0. We construct Abelian functions…

General derivative Thomae formula for singular half-periods

- MathematicsLetters in Mathematical Physics
- 2020

The paper develops second Thomae theorem in hyperelliptic case. The main formula, called general Thomae formula, provides expressions for values at zero of the lowest non-vanishing derivatives of…

ON DEGENERATE SIGMA-FUNCTIONS IN GENUS 2

- MathematicsGlasgow Mathematical Journal
- 2018

Abstract We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus 1 sigma-function and elementary functions as solutions of a system of linear partial differential…

Building Abelian Functions with Generalised Baker-Hirota Operators

- Mathematics
- 2012

We present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear operator defined…

Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-times

- Physics
- 2010

All observations in the gravitational domain can be explained by means of Einstein’s General Relativity. While for small scale gravitational effects (e.g. in the solar system) the standard Einstein…

Generalized Lie Theory In Mathematics, Physics And Beyond

- Mathematics
- 2009

Non-Associative and Non-Commutative Structures for Physics.- Moufang Transformations and Noether Currents.- Weakly Nonassociative Algebras, Riccati and KP Hierarchies.- Applications of…

Applications of Transvectants

- Mathematics
- 2009

We discuss the role of the transvectant, a device dating from the early history of representation theory, in the theory of Pade approximants and hyperelliptic p-functions.