Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 037, 36 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.037
(Mi sigma714)
 

This article is cited in 2 scientific papers (total in 2 papers)

Building Abelian functions with generalised Baker–Hirota operators

Matthew Englanda, Chris Athorneb

a Department of Computer Science, University of Bath, Bath, BA2 7AY, UK
b School of Mathematics and Statistics, University of Glasgow, G12 8QQ, UK
Full-text PDF (554 kB) Citations (2)
References:
Abstract: 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 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.
Keywords: Baker–Hirota operator, $\mathcal R$-function, Abelian function, Kleinian function.
Received: March 16, 2012; in final form June 18, 2012; Published online June 26, 2012
Bibliographic databases:
Document Type: Article
MSC: 14H40; 14H50; 14H70
Language: English
Citation: Matthew England, Chris Athorne, “Building Abelian functions with generalised Baker–Hirota operators”, SIGMA, 8 (2012), 037, 36 pp.
Citation in format AMSBIB
\Bibitem{EngAth12}
\by Matthew England, Chris Athorne
\paper Building Abelian functions with generalised Baker--Hirota operators
\jour SIGMA
\yr 2012
\vol 8
\papernumber 037
\totalpages 36
\mathnet{http://mi.mathnet.ru/sigma714}
\crossref{https://doi.org/10.3842/SIGMA.2012.037}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2946863}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000305602400001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864107623}
Linking options:
  • https://www.mathnet.ru/eng/sigma714
  • https://www.mathnet.ru/eng/sigma/v8/p37
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:226
    Full-text PDF :47
    References:52
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024