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The k-dimensional Duffin and Schaeffer conjecture

Published online by Cambridge University Press:  26 February 2010

A. D. Pollington  and
R. C. Vaughan
A. D. Pollington
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah, 84602, U.S.A.
R. C. Vaughan
Affiliation:
Department of Mathematics, Imperial College, London, SW7 2BZ
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Extract

In 1941 Duffin and Schaeffer [2] considered the case k = 1 of the assertion that when the statement;

(Ak) “For almost all there are infinitely many natural numbers q for which there exist integers a1,…, ak such that (a1 … ak, q) = 1 and

where

holds, if, and only if,

diverges.

Type
Research Article
Information
Mathematika , Volume 37 , Issue 2 , December 1990 , pp. 190 - 200
Copyright
Copyright © University College London 1990

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References

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