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 Tr. Mat. Inst. Steklova, 2009, Volume 266, Pages 5–32 (Mi tm1883)

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:

UDC: 515.178.2+517.958

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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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
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
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
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