This article is cited 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.

UDC: 511

Received: 24.06.2013