Heat equations and families of two-dimensional sigma functions (Q1048441)

The paper is devoted to constructing a system of differential equations that describes a relationship between the parameters of two-dimensional theta and sigma functions. The authors used the classical system of heat equations, which holds for the theta function, and the system of heat equations in a nonholonomic frame which holds the sigma function. The approach is based on the fact that, under the additional requirement of quasiperiodicity of solutions, these systems characterize theta and sigma functions, respectively.