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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.

Constructions of smooth and analytic cocycles over irrational circle rotations

Dalibor Volný (1995)

Commentationes Mathematicae Universitatis Carolinae

We define a class of step cocycles (which are coboundaries) for irrational rotations of the unit circle and give conditions for their approximation by smooth and real analytic coboundaries. The transfer functions of the approximating (smooth and real analytic) coboundaries are close (in the supremum norm) to the transfer functions of the original ones. This result makes it possible to construct smooth and real analytic cocycles which are ergodic, ergodic and squashable (see [Aaronson, Lemańczyk,...

Coprimality of integers in Piatetski-Shapiro sequences

Watcharapon Pimsert, Teerapat Srichan, Pinthira Tangsupphathawat (2023)

Czechoslovak Mathematical Journal

We use the estimation of the number of integers n such that n c belongs to an arithmetic progression to study the coprimality of integers in c = { n c } n , c > 1 , c .

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