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# Communications in Number Theory and Physics

## Volume 13 (2019)

### Number 1

### Approximating tau-functions by theta-functions

Pages: 203 – 223

DOI: https://dx.doi.org/10.4310/CNTP.2019.v13.n1.a7

#### Author

#### Abstract

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.

#### Keywords

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