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.

中文翻译：

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通过 theta 函数逼近 tau 函数

我们证明，在分级形式级数的拓扑中，可以通过有限属的超椭圆 theta 函数的对数展开来近似 KdV 层次结构的任意 tau 函数的对数，最多可达二次项。作为一个例子，我们考虑 Witten--Kontsevich tau 函数的 theta 函数近似。