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On the distribution of αpk modulo 1

Published online by Cambridge University Press:  18 May 2009

K. C. Wong
K. C. Wong
Affiliation:
School of Mathematics, University of Wales, College of Cardiff, Senghenydd Road, Cardiff CF2 4AG.
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The fractional part of the sequence {αnk}, where α is an irrational real number and k is an integer, was first studied early this century, initiated by the work of Hardy, Littlewood and Weyl. It seems very natural to consider the subsequence {αpk}, where p denotes a prime variable. The pioneering work in this direction was conducted by Vinogradov [13,14]. Improvements have since been made by Vaughan [12], Ghosh [4], Harman [6,7,8] and Jia [11]. The best results to date have been obtained by Harman for k = 1 [9], by Baker and Harman for 2 ≤ k ≤ 12 [1], and by Harman for larger k [8]. In the following work, we shall adopt a sieve technique developed by Harman in [6] to show the following.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 2 , May 1997 , pp. 121 - 130
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

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