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

B. Dubrovin (Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy; and the N.N. Bogolyubov Laboratory of Geometrical Methods in Mathematical Physics, Moscow State University, Moscow, Russia)

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.

Full Text (PDF format)

Received 18 July 2018

Accepted 24 October 2018

Published 29 April 2019