Higher genus Abelian functions associated with cyclic trigonal curves

Matthew England

doi:10.3842/SIGMA.2010.025

Higher genus Abelian functions associated with cyclic trigonal curves

Matthew England

University of Glasgow

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula.

Original language	English
Article number	025
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	6
DOIs	https://doi.org/10.3842/SIGMA.2010.025
Publication status	Published - 2010
Externally published	Yes

Keywords

Abelian function
Cyclic trigonal curve
Jacobi inversion problem
Kleinian sigma function

ASJC Scopus subject areas

Analysis
Geometry and Topology
Mathematical Physics

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10.3842/SIGMA.2010.025

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title = "Higher genus Abelian functions associated with cyclic trigonal curves",

abstract = "We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula.",

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AB - We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula.

KW - Abelian function

KW - Cyclic trigonal curve

KW - Jacobi inversion problem

KW - Kleinian sigma function

U2 - 10.3842/SIGMA.2010.025

DO - 10.3842/SIGMA.2010.025

M3 - Article

AN - SCOPUS:84896059136

SN - 1815-0659

VL - 6

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 025

ER -

Higher genus Abelian functions associated with cyclic trigonal curves

Abstract

Keywords

ASJC Scopus subject areas

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