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Characterizations of groups generated by Kronecker sets

András Biró (2007)

Journal de Théorie des Nombres de Bordeaux

In recent years, starting with the paper [B-D-S], we have investigated the possibility of characterizing countable subgroups of the torus T = R / Z by subsets of Z . Here we consider new types of subgroups: let K T be a Kronecker set (a compact set on which every continuous function f : K T can be uniformly approximated by characters of T ), and G the group generated by K . We prove (Theorem 1) that G can be characterized by a subset of Z 2 (instead of a subset of Z ). If K is finite, Theorem 1 implies our earlier result...

Concentration function of additive functions on shifted twin primes

Simon Wong (1998)

Acta Arithmetica

0. Introduction. The content of this paper is part of the author's Ph.D. thesis. The two new theorems in this paper provide upper bounds on the concentration function of additive functions evaluated on shifted γ-twin prime, where γ is any positive even integers. Both results are generalizations of theorems due to I. Z. Ruzsa, N. M. Timofeev, and P. D. T. A. Elliott.

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