Difference between revisions of "Algebraic independence, measure of"
From Encyclopedia of Mathematics
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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 [[ | + | 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
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