On the Fractional Parts of a Polynomial
1976 ◽
Vol 28
(1)
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pp. 168-173
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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 satisfyingwhere ||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]).
1972 ◽
Vol 72
(2)
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pp. 209-212
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1978 ◽
Vol 36
(1)
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pp. 176-177
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1990 ◽
Vol 48
(2)
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pp. 540-541
1960 ◽
Vol 27
(1)
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pp. 19-32
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2011 ◽
Vol 85
(3)
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pp. 463-475
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1966 ◽
Vol 62
(4)
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pp. 637-642
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1962 ◽
Vol 14
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pp. 565-567
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