, Volume 266, Issue 1, pp 1-28
Date: 10 Oct 2009

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.

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.