On the Distribution of Primitive Lattice Points in the Plane
Canadian mathematical bulletin, Tome 2 (1959) no. 2, pp. 91-96
Voir la notice de l'article provenant de la source Cambridge University Press
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
Chalk, J.H.H.; Erdos, P. On the Distribution of Primitive Lattice Points in the Plane. Canadian mathematical bulletin, Tome 2 (1959) no. 2, pp. 91-96. doi: 10.4153/CMB-1959-014-7
@article{10_4153_CMB_1959_014_7,
author = {Chalk, J.H.H. and Erdos, P.},
title = {On the {Distribution} of {Primitive} {Lattice} {Points} in the {Plane}},
journal = {Canadian mathematical bulletin},
pages = {91--96},
year = {1959},
volume = {2},
number = {2},
doi = {10.4153/CMB-1959-014-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-014-7/}
}
TY - JOUR AU - Chalk, J.H.H. AU - Erdos, P. TI - On the Distribution of Primitive Lattice Points in the Plane JO - Canadian mathematical bulletin PY - 1959 SP - 91 EP - 96 VL - 2 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1959-014-7/ DO - 10.4153/CMB-1959-014-7 ID - 10_4153_CMB_1959_014_7 ER -
[1] 1. Cassels, J.W.S., Ueber lim x|θx+α-y|, Math, Annalen 127 (1954), 288. Google Scholar
[2] 2. Chalk, J.H.H., Introduction to Cambridge Ph.D. thesis, 1951, Theorem 4. Google Scholar
[3] 3. Erdös, P., On an elementary problem in number theory, Canadian Math. Bull. 1, (1958), 5-8. Google Scholar
[4] 4. Hardy, G.H. and Wright, E.M., Introduction to the Theory of Numbers, (Oxford, 1945), Ch XXIII, Theorems 442, 444. Google Scholar
[5] 5. Koksma, J.F., Diophantische Approximationen, Ergebnisse der Mathematik, Bd. IV, Ht. 4, (Berlin, 1937). Google Scholar
Cité par Sources :