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On the Distribution of Primitive Lattice Points in the Plane

Published online by Cambridge University Press:  20 November 2018

J.H.H. Chalk  and
P. Erdos
J.H.H. Chalk
Affiliation:
McMaster University
P. Erdos
Affiliation:
McMaster University
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Let 1,θ1, θ2, …,θn be real numbers linearly independent over the rational field and let α1, α2,…, αn be arbitrary real numbers. Then, to each N > 0 and ε > 0, there correspond integers

which satisfy the set of inequalities

A

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 2 , Issue 2 , 01 May 1959 , pp. 91 - 96
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Cassels, J.W.S., Ueber lim x|θx+α-y|, Math, Annalen 127 (1954), 288.Google Scholar
2. Chalk, J.H.H., Introduction to Cambridge Ph.D. thesis, 1951, Theorem 4.Google Scholar
3. Erdös, P., On an elementary problem in number theory, Canadian Math. Bull. 1, (1958), 5-8.Google Scholar
4. Hardy, G.H. and Wright, E.M., Introduction to the Theory of Numbers, (Oxford, 1945), Ch XXIII, Theorems 442, 444.Google Scholar
5. Koksma, J.F., Diophantische Approximationen, Ergebnisse der Mathematik, Bd. IV, Ht. 4, (Berlin, 1937).Google Scholar