Geodesic
On the Fractional Parts of a Polynomial
Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 168-173

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

Heilbronn [6] proved that for any ε > 0 there exists C(ε) such that for any real θ and N ≧ 1 there is an integer x satisfying where ||α|| denotes the difference between α and the nearest integer, taken positively. Danicic [2] obtained an analogous result for the fractional parts of θxk and in 1967 Davenport [4] generalized Heilbronn's result to polynomials of degree with no constant term. The last condition is essential, for if there is a constant term then no analogous result can hold (see Koksma [7, Kap. 6 SatzlO]). 
Cook, R. J. On the Fractional Parts of a Polynomial. Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 168-173. doi: 10.4153/CJM-1976-021-2
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