Geodesic
On the fractional parts of αn2 and βn
Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 181-183

Voir la notice de l'article provenant de la source Cambridge University Press

We denote by ‖...‖ the distance to the nearest integer. Let α and β be real. W. M. Schmidt [5] proved that for ε > 0 and N>c1(ε) there is a natural number n such thatThis extends a theorem of H. Heilbronn [4] and also sharpens a theorem of H. Davenport [3]. 
Baker, R. C. On the fractional parts of αn2 and βn. Glasgow mathematical journal, Tome 22 (1981) no. 2, pp. 181-183. doi: 10.1017/S0017089500004651
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[1] 1.Baker, R. C., Recent results on fractional parts of polynomials, Number theory, Carbondale 1979, Lecture Notes in Mathematics No. 751 (Springer-Verlag, 1979), 10–18. Google Scholar | DOI

[2] 2.Baker, R. C. and Gajraj, J., Some non-linear Diophantine approximations. Acta Arith. 31 (1976), 325–341. Google Scholar | DOI

[3] 3.Davenport, H., On a theorem of Heilbronn, Quart. J. Math. Oxford Ser. 2, 18 (1967), 339–344. Google Scholar | DOI

[4] 4.Heilbronn, H., On the distribution of the sequence n2θ(mod 1), Quart. J. Math. Oxford Ser. 1, 19 (1948), 249–256. Google Scholar | DOI

[5] 5.Schmidt, W. M., On the distribution modulo 1 of die sequence αn2 + βn, Canad. J. Math. 29 (1977), 819–826. Google Scholar | DOI

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