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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 20568, 20 pages
http://dx.doi.org/10.1155/IJMMS/2006/20568

Dispersion properties of ergodic translations

Dipartimento di Matematica e Informatica, Università di Camerino, via Madonna delle Carceri, Camerino 62032, Italy

Received 19 November 2005; Revised 23 January 2006; Accepted 25 January 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider irrational rotations of the circle Tx=x+α (mod 1) and study the asymptotic behavior of sums of the type Sn=k=0n1πk with πk=±1, the sign being determined by the location of Tkx with respect to a binary partition.