Binomial-coefficient multiples of irrationals

Details Binomial-coefficient multiples of irrationals Binomial-coefficient multiples of irrationals

1998-06-18

arxiv.org/abs/math/9806098v1

Montashefte f. Mathematik 125 (1998), 269-278.

Mathematics

Dynamical Systems

10 pages, to appear in Monatshefte f. Math

Scientific paper

Denote by $x$ a random infinite path in the graph of Pascal's triangle (left
and right turns are selected independently with fixed probabilities) and by
$d_n(x)$ the binomial coefficient at the $n$'th level along the path $x$. Then
for a dense $G_{\delta}$ set of $\theta$ in the unit interval, $\{d_n(x)\theta
\}$ is almost surely dense but not uniformly distributed modulo 1.

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