# Algebraic independence, measure of

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.