FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

Multiplicity estimates for theta constants

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