Weyl criterion
From Encyclopedia of Mathematics
A fundamental criterion used to solve the problem of the uniform distribution of an infinite sequence of arbitrary real numbers
modulo
, i.e. to establish the existence of the limit
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where and
is the fractional part of
(cf. Fractional part of a number). According to Weyl's criterion, the sequence
is uniformly distributed modulo
if and only if
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for all integers . Demonstrated in 1916 by H. Weyl. See Weyl method.
References
[1] | J.W.S. Cassels, "An introduction to diophantine approximation" , Cambridge Univ. Press (1957) |
How to Cite This Entry:
Weyl criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Weyl_criterion&oldid=30171
Weyl criterion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Weyl_criterion&oldid=30171
This article was adapted from an original article by B.M. Bredikhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article