Communications in Number Theory and Physics
Volume 13 (2019)
Approximating tau-functions by theta-functions
Pages: 203 – 223
We prove that the logarithm of an arbitrary tau-function of the KdV hierarchy can be approximated, in the topology of graded formal series by the logarithmic expansions of hyperelliptic theta-functions of finite genus, up to at most quadratic terms. As an example, we consider theta-functional approximations of the Witten–Kontsevich tau-function.
The work is supported by the Russian Science Foundation Grant No. 16-11-10260 “Geometry and Mathematical Physics of Integrable Systems”.
2010 Mathematics Subject Classification
Primary 37K10. Secondary 14K25.
Received 18 July 2018
Accepted 24 October 2018
Published 29 April 2019