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Tr. Mat. Inst. Steklova, 2009, Volume 266, Pages 5–32 (Mi tm1883)  
This article is cited in 3 scientific papers (total in 3 papers)

Heat Equations and Families of Two-Dimensional Sigma Functions

E. Yu. Bunkova, V. M. Buchstaber

Steklov Institute of Mathematics, Russian Academy of Sciences, Moscow, Russia

Abstract: In the framework of S. P. Novikov's program for boosting the effectiveness of theta-function formulas of finite-gap integration theory, a system of differential equations for the parameters of the sigma function in genus 2 is constructed. A counterpart of this system in genus 1 is equivalent to the Chazy equation. On the basis of the obtained results, a two-dimensional analog of the Frobenius–Stickelberger connection is defined and calculated.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2009, 266, 1–28

Bibliographic databases:

Document Type: Article
UDC: 515.178.2+517.958
Received in April 2009

Citation: E. Yu. Bunkova, V. M. Buchstaber, “Heat Equations and Families of Two-Dimensional Sigma Functions”, Geometry, topology, and mathematical physics. II, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 266, MAIK Nauka/Interperiodica, Moscow, 2009, 5–32; Proc. Steklov Inst. Math., 266 (2009), 1–28

Citation in format AMSBIB
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\paper Heat Equations and Families of Two-Dimensional Sigma Functions
\inbook Geometry, topology, and mathematical physics.~II
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2009
\vol 266
\pages 5--32
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    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. Buchstaber V.M., “Heat Equations and Sigma Functions”, Geometric Methods in Physics, AIP Conference Proceedings, 1191, 2009, 46–58  crossref  adsnasa  isi  scopus
    2. E. Yu. Bunkova, V. M. Buchstaber, “Polynomial Dynamical Systems and Ordinary Differential Equations Associated with the Heat Equation”, Funct. Anal. Appl., 46:3 (2012), 173–190  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. E. Yu. Netay, “Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2”, Trans. Moscow Math. Soc., 74 (2013), 281–292  mathnet  crossref  mathscinet  zmath  elib
    		• Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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