FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 2, PAGES 557-562

Yu. V. Nesterenko

Abstract

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```
An upper bound for multiplicity of zero at the point
```$q=0$ for
polynomials in logarithmic derivatives of theta constants
is proved. The upper bound depends on degrees of the polynomials.
The proof is based on a description
in terms of theta constants of the general solution of
a system of algebraic differential equations.

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Last modified: July 6, 1999