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Linear independence, measure of

From Encyclopedia of Mathematics
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of numbers

The function

where the minimum is taken over all possible sets of integers satisfying the conditions

It is known that

where if all the numbers are real, and otherwise. To obtain lower bounds of with respect to the parameter for specific sets of numbers is one of the problems of the theory of Diophantine approximations.

How to Cite This Entry:
Linear independence, measure of. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_independence,_measure_of&oldid=34658
This article was adapted from an original article by Yu.V. Nesterenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article