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Heat equations and families of two-dimensional sigma functions

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Abstract

In the framework of S.P. Novikov’s program for boosting the effectiveness of thetafunction 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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Authors and Affiliations

  1. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    E. Yu. Bunkova & V. M. Buchstaber

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  1. E. Yu. Bunkova
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  2. V. M. Buchstaber
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Correspondence to E. Yu. Bunkova.

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Original Russian Text © E.Yu. Bunkova, V.M. Buchstaber, 2009, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 266, pp. 5–32.

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Bunkova, E.Y., Buchstaber, V.M. Heat equations and families of two-dimensional sigma functions. Proc. Steklov Inst. Math. 266, 1–28 (2009). https://doi.org/10.1134/S0081543809030018

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