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Chebyshevskii Sb., 2013, Volume 14, Issue 2, Pages 68–73 (Mi cheb270)  

This article is cited in 1 scientific paper (total in 1 paper)

Perfect squares of the form $[\alpha n]$

D. V. Goryashin

M. V. Lomonosov Moscow State University

Abstract: An asymptotic formula is proved for the number of perfect squares in the sequence $[\alpha n]$ for algebraic numbers $\alpha$ and irrational numbers $\alpha$ with restricted partial quotients.

Keywords: perfect squares, Beatty sequence, asymptotic formula, exponential sums, Weyl sums.

Full text: PDF file (224 kB)
References: PDF file   HTML file
UDC: 511
Received: 24.06.2013

Citation: D. V. Goryashin, “Perfect squares of the form $[\alpha n]$”, Chebyshevskii Sb., 14:2 (2013), 68–73

Citation in format AMSBIB
\Bibitem{Gor13}
\by D.~V.~Goryashin
\paper Perfect squares of the form $[\alpha n]$
\jour Chebyshevskii Sb.
\yr 2013
\vol 14
\issue 2
\pages 68--73
\mathnet{http://mi.mathnet.ru/cheb270}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Begunts, D. V. Goryashin, “Aktualnye zadachi, svyazannye s posledovatelnostyami Bitti”, Chebyshevskii sb., 18:4 (2017), 97–106  mathnet  crossref
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