Geodesic
On the number of points of an incomplete lattice in rectangular regions
Čebyševskij sbornik, Tome 25 (2024) no. 4, pp. 138-146 Cet article a éte moissonné depuis la source Math-Net.Ru

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In 2013–2015 it was shown that for any purely real algebraic irrationality $\alpha$, starting from some place, all residual fractions in the expansion of $\alpha$ into a continued fraction will appear to be the reduced algebraic irrationalities. We construct the examples of purely real algebraic irrationalities $\alpha$ for which this number of the residual fraction is arbitrarily large.
Keywords: purely real algebraic irrationality, reduced algebraic irrationality. 
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     author = {N. N. Dobrovol'skii and N. M. Dobrovol'skii},
     title = {On the number of points of an incomplete lattice in rectangular regions},
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N. N. Dobrovol'skii; N. M. Dobrovol'skii. On the number of points of an incomplete lattice in rectangular regions. Čebyševskij sbornik, Tome 25 (2024) no. 4, pp. 138-146. http://geodesic.mathdoc.fr/item/CHEB_2024_25_4_a7/