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A problem of Hooley in Diophantine approximation

Published online by Cambridge University Press:  18 May 2009

Glyn Harman
Glyn Harman
Affiliation:
School of Mathematics, 23 Senghennydd Road, P.O. Box 926, Cardiff CF2 4YH, Wales, E-Mail: [email protected]
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In [5] Professor Hooley announced without proof the following result which is a variant of well-known work by Heilbronn [4]and Danicic [3] (see [1]).

Let k≥2 be an integer, b a fixed non-zero integer, and a an irrational real number. Then, for any ɛ> 0, there are infinitely many solutions to the inequality

Here

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 3 , September 1996 , pp. 299 - 308
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

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