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Binomial-coefficient multiples of irrationals

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Abstract

Denote byx a random infinite path in the graph of Pascal's triangle (left and right turns are selected independently with fixed probabilities) and byd n (x) the binomial coefficient at then'th level along the pathx. Then for a denseG 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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  1. Terrence M. Adams

    Present address: Department of Mathematics, Ohio State University, 43210, Columbus, OH, USA

Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, CB 3250 Phillips Hall, 27599-3250, Chapel Hill, NC, USA

    Terrence M. Adams & Karl E. Petersen

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  1. Terrence M. Adams
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  2. Karl E. Petersen
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Adams, T.M., Petersen, K.E. Binomial-coefficient multiples of irrationals. Monatshefte für Mathematik 125, 269–278 (1998). https://doi.org/10.1007/BF01305342

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