Geodesic
On the Distribution Modulo 1 of the Sequence αn 2 + βn
Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 819-826

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

Dirichlet's Theorem says that for any real α and for N ≧ 1, there exists a natural n ≦ N with where || || denotes the distance to the nearest integer. Heilbronn [2], improving estimates of Vinogradov [3], showed that for α, N as above and for ε ≧ 0, there exists an n ≦ N with 
Schmidt, Wolfgang M. On the Distribution Modulo 1 of the Sequence αn 2 + βn. Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 819-826. doi: 10.4153/CJM-1977-084-8
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[1] 1. Davenport, H., On a theorem of Heilbronn, Quart. J. Math. (2) 18 (1967), 337–344. Google Scholar

[2] 2. Heilbronn, H., On the distribution of the sequence n∼d (mod 1), Quart. J. Math. 10 (1948), 249–2.56. Google Scholar

[3] 3. Vinogradov, I. M., Analytischer Beweis des Satzes iiber die Verteilung der Bruchteile eines ganzen Polynonis, Bull. Acad. Sci. USSR (6) 21 (1927), 567–578. Google Scholar

[4] 4. Vinogradov, I. M., The method of trigonometric sums in the theory of numbers (1947), English transi. (Interscience, New York, 1954). Google Scholar

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