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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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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DOI: https://doi.org/10.1134/S0081543809030018