# Algebraic independence, measure of

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 11J82 [MSN][ZBL]

The measure of algebraic independence of the numbers $\alpha_1,\dots,\alpha_m$ is the function

$$\Phi(\alpha_1,\dots,\alpha_m;n,H)=\min|P(\alpha_1,\dots,\alpha_m)|,$$

where the minimum is taken over all polynomials of degree at most $n$, with rational integer coefficients not all of which are zero, and of height at most $H$. For more details see Transcendency, measure of.

**How to Cite This Entry:**

Algebraic independence, measure of.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Algebraic_independence,_measure_of&oldid=35743

This article was adapted from an original article by A.B. Shidlovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article