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Metric Diophantine approximation with two restricted variables II: A prime and a square-free integer

Published online by Cambridge University Press:  26 February 2010

Glyn Harman
Glyn Harman
Affiliation:
Department of Pure Mathematics, University College, P.O. Box 78, Cardiff CF1 1XL.
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Extract

In this paper we continue the investigation begun in [6] concerning the number of solutions of the inequality

for almost all α (in the sense of Lebesgue measure on ℝ), where β is a given real number, , and both m and n are confined to sets of numbertheoretic interest. Our aim is to extend existing results ([7], [8], [5] for example), where only n is restricted. Here we shall prove the following result where, as elsewhere in this paper, p denotes a prime, and a square-free integer may be positive or negative.

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Type
Research Article
Information
Mathematika , Volume 35 , Issue 1 , June 1988 , pp. 59 - 68
Copyright
Copyright © University College London 1988

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References

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