Binomial-coefficient multiples of irrationals

1998/06/18 by Terrence M. Adams, Karl E. Petersen
Mathematics · #math.DS #math.NT

paper · pdf

published as Montashefte f. Mathematik 125 (1998), 269-278. · 10 pages, to appear in Monatshefte f. Math

arxiv created 1998/06/18 · arxiv updated 2009/11/30

Abstract

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_δ set of θ in the unit interval, \d_n(x)θ\ is almost surely dense but not uniformly distributed modulo 1.

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