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


SIGMA, 2012, Volume 8, 037, 36 pages (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

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.

DOI: https://doi.org/10.3842/SIGMA.2012.037

Full text: PDF file (554 kB)
Full text: http://emis.mi.ras.ru/.../037
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 1203.3409
MSC: 14H40; 14H50; 14H70
Received: March 16, 2012; in final form June 18, 2012; Published online June 26, 2012
Language:

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://www.ams.org/mathscinet-getitem?mr=2946863}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305602400001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864107623}


Linking options:
  • http://mi.mathnet.ru/eng/sigma714
  • http://mi.mathnet.ru/eng/sigma/v8/p37

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Levin, M. A. Olshanetskii, A. V. Zotov, “Klassifikatsiya izomonodromnykh zadach na ellipticheskikh krivykh”, UMN, 69:1(415) (2014), 39–124  mathnet  crossref  mathscinet  zmath  elib
    2. Eilbeck J.Ch., England M., Onishi Y., “Some New Addition Formulae For Weierstrass Elliptic Functions”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 470:2171 (2014), 20140051  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:136
    Full text:25
    References:32

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019