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JOURNALS // Chebyshevskii Sbornik // Archive

Chebyshevskii Sb., 2013 Volume 14, Issue 3, Pages 42–48 (Mi cheb287)

This article is cited in 2 papers

Squarefree numbers in the sequence $[\alpha n]$

D. V. Goryashin

M. V. Lomonosov Moscow State University

Abstract: An asymptotic formula for the number of squarefree integers of the form $[\alpha n]$ is proved in the paper, where $\alpha$ is an algebraic number or a number with restricted partial quotients.

Keywords: squarefree numbers, Beatty sequence, asymptotic formula, exponential sums.

UDC: 511

Received: 18.09.2013



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