Heat equations and families of two-dimensional sigma functions



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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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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