Namespaces
Variants
Actions

Difference between revisions of "Algebraic independence, measure of"

From Encyclopedia of Mathematics
Jump to: navigation, search
(TeX)
(MSC 11J82)
 
Line 1: Line 1:
{{TEX|done}}
+
{{TEX|done}}{{MSC|11J82}}
 +
 
 
The measure of algebraic independence of the numbers $\alpha_1,\dots,\alpha_m$ is the function
 
The measure of algebraic independence of the numbers $\alpha_1,\dots,\alpha_m$ is the function
  
 
$$\Phi(\alpha_1,\dots,\alpha_m;n,H)=\min|P(\alpha_1,\dots,\alpha_m)|,$$
 
$$\Phi(\alpha_1,\dots,\alpha_m;n,H)=\min|P(\alpha_1,\dots,\alpha_m)|,$$
  
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|Transcendency, measure of]].
+
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]].

Latest revision as of 15:41, 20 December 2014

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=33284
This article was adapted from an original article by A.B. Shidlovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article