Binomial-coefficient multiples of irrationals
Copyright policy )Binomial-coefficient multiples of irrationals
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 $G_��$ set of $��$ in the unit interval, $\{d_n(x)��\}$ is almost surely dense but not uniformly distributed modulo 1.
10 pages, to appear in Monatshefte f. Math
- DigiZeitschriften Germany
- University of North Carolina at Chapel Hill United States
Pascal-adic transformation, Pascal graph, Pascal triangle, Mathematics - Number Theory, Dynamical aspects of measure-preserving transformations, Dynamical Systems (math.DS), Measure-preserving transformations, Article, 510.mathematics, FOS: Mathematics, invariant ergodic measures, Relations of ergodic theory with number theory and harmonic analysis, Number Theory (math.NT), Mathematics - Dynamical Systems, Bernoulli measures, General theory of distribution modulo \(1\)
Pascal-adic transformation, Pascal graph, Pascal triangle, Mathematics - Number Theory, Dynamical aspects of measure-preserving transformations, Dynamical Systems (math.DS), Measure-preserving transformations, Article, 510.mathematics, FOS: Mathematics, invariant ergodic measures, Relations of ergodic theory with number theory and harmonic analysis, Number Theory (math.NT), Mathematics - Dynamical Systems, Bernoulli measures, General theory of distribution modulo \(1\)
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