A Metrical Theorem in Diophantine Approximation
- 1 January 1960
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 12, 619-631
- https://doi.org/10.4153/cjm-1960-056-0
Abstract
In this paper we prove a sharpening and generalization of the following Theorem of Khintchine (4):Let ψ1(q), …, ψnq) be n non-negative junctions of the positive integer q and assume is monotonically decreasing. Then the set of inequalities 1 has an infinity of integer solutions q > 0 and p1, … , pn for almost all or no sets of numbers θ1, … , θ2, according as Σψ(q) diverges or converges.Keywords
This publication has 3 references indexed in Scilit:
- Some metrical theorems in Diophantine approximation. IIIMathematical Proceedings of the Cambridge Philosophical Society, 1950
- Some metrical theorems in Diophantine approximation. IMathematical Proceedings of the Cambridge Philosophical Society, 1950
- Zur metrischen Theorie der diophantischen ApproximationenMathematische Zeitschrift, 1926