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Irrational dilations of Pascal's triangle

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  26 February 2010

D. Berend ,
M. D. Boshernitzan  and
G. Kolsenik
D. Berend
Affiliation:
Departments of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
M. D. Boshernitzan
Affiliation:
Department of Mathematics, Rice University, Houston, Texas 77251, USA.
G. Kolsenik
Affiliation:
Department of Mathematics and Computer Science, California State University, Los Angeles, CA 90032, USA.
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Extract

Let (bn) be a sequence of integers, obtained by traversing the rows of Pascal's triangle, as follows: start from the element at the top of the triangle, and at each stage continue from the current element to one of the elements at the next row, either the one immediately to the left of the current element or the one immediately to its right. Consider the distribution of the sequence (bnα) modulo 1 for an irrational α. The main results show that this sequence “often” fails to be uniformly distributed modulo 1, and provide answers to some questions raised by Adams and Petersen.

MSC classification

Secondary: 11J71: Distribution modulo one
Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 159 - 168
Copyright
Copyright © University College London 2001

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