View source for Algebraic independence, measure of

The measure of algebraic independence of the numbers <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011540/a0115401.png" /> is the function

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011540/a0115402.png" /></td> </tr></table>

where the minimum is taken over all polynomials of degree at most <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011540/a0115403.png" />, with rational integer coefficients not all of which are zero, and of height at most <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a011/a011540/a0115404.png" />. For more details see [[Transcendency, measure of|Transcendency, measure of]].