TY - JOUR

T1 - Building Abelian Functions with Generalised Baker-Hirota Operators

AU - England, Matthew

AU - Athorne, C

PY - 2012

Y1 - 2012

N2 - 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 in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operators, use them to define infinite sequences of Abelian functions of a prescribed pole structure and deduce the key properties of these functions. We apply the theory on the two canonical curves of genus three, presenting new explicit examples of vector space bases of Abelian functions. These reveal previously unseen similarities between the theories of functions associated to curves of the same genus.

AB - 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 in the work of Baker and Hirota. We give explicit formulae for the multiple applications of the operators, use them to define infinite sequences of Abelian functions of a prescribed pole structure and deduce the key properties of these functions. We apply the theory on the two canonical curves of genus three, presenting new explicit examples of vector space bases of Abelian functions. These reveal previously unseen similarities between the theories of functions associated to curves of the same genus.

UR - http://www.scopus.com/inward/record.url?scp=84864107623&partnerID=8YFLogxK

UR - http://arxiv.org/abs/1203.3409

UR - http://dx.doi.org/10.3842/SIGMA.2012.037

U2 - 10.3842/SIGMA.2012.037

DO - 10.3842/SIGMA.2012.037

M3 - Article

SN - 1815-0659

VL - 8

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

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

IS - 037

ER -