From: lerma@math.nwu.edu (Miguel A. Lerma)
Subject: Re: Prime square roots...
Date: 18 Jun 1999 12:48:10 GMT
Newsgroups: sci.math
Keywords: Fejer's theorem (sequences mod 1)
Miguel A. Lerma (lerma@math.nwu.edu) wrote:
: The sequence sqrt(n) is uniformly distributed modulo 1, so the
: result is the same.
Let me add that this is a consequence of Fejer's theorem: Let f(x)
be a function defined for x>=1 that is differentiable for x>=x0.
If f'(x) tends monotonically to 0 as x -> infinity and if x|f'(x)|
-> infinity as x -> infinity, then the sequence f(n), n=1,2,3,...,
is uniformly distributed modulo 1. See L. Kuipers & H. Niederreiter:
"Uniform distribution of Sequences".
Miguel A. Lerma