Displaying similar documents to “On the distribution of a sequence in a compact group”

On the fractional parts of x / n and related sequences. I

Bahman Saffari, R. C. Vaughan (1976)

Annales de l'institut Fourier

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This paper and its sequels deal with a new concept of distributions modulo one which is connected with the Dirichlet divisor and similar problems. Each of the theorems has some independent interest, and in addition some of the techniques developed lead to improvements in certain applications of the hyperbola method.

Aspects of uniformity in recurrence

Vitaly Bergelson, Bernard Host, Randall McCutcheon, Franiçois Parreau (2000)

Colloquium Mathematicae

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We analyze and cite applications of various, loosely related notions of uniformity inherent to the phenomenon of (multiple) recurrence in ergodic theory. An assortment of results are obtained, among them sharpenings of two theorems due to Bourgain. The first of these, which in the original guarantees existence of sets x,x+h, x + h 2 in subsets E of positive measure in the unit interval, with lower bounds on h depending only on m(E), is expanded to the case of arbitrary finite polynomial configurations...