The fractional parts of an additive form
1972 ◽
Vol 72
(2)
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pp. 209-212
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Keyword(s):
Heilbronn (6) proved that for every ε ≥ 0 and N ≥ 1 and every real θ there is an integer x such that,where C(ε) depends only on ε and ∥α∥ is the difference between α and the nearest integer, taken positively. Danicic(1) obtained an analogous result for the fractional parts of nkθ, the proof of this is more readily accessible in Davenport(4). Danicic(2) also obtained an estimate for the fractional parts of a real quadratic form in n variables, and in order to extend this result to forms of higher degree it is desirable to first obtain results for additive forms.
1984 ◽
Vol 96
(2)
◽
pp. 213-222
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1958 ◽
Vol 54
(1)
◽
pp. 14-17
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Keyword(s):
1976 ◽
Vol 28
(1)
◽
pp. 168-173
◽
1978 ◽
Vol 36
(1)
◽
pp. 176-177
Keyword(s):
1990 ◽
Vol 48
(2)
◽
pp. 540-541
1960 ◽
Vol 27
(1)
◽
pp. 19-32
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Keyword(s):
2011 ◽
Vol 85
(3)
◽
pp. 463-475
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Keyword(s):
1955 ◽
Vol 7
◽
pp. 337-346
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1966 ◽
Vol 62
(4)
◽
pp. 637-642
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Keyword(s):