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The distribution of αp modulo one

Published online by Cambridge University Press:  01 September 2009

KAISA MATOMÄKI
KAISA MATOMÄKI*
Affiliation:
Department of Mathematics, 20014 University of Turku, Finland. e-mail: ksmato@utu.fi
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Abstract

We prove that, for any irrational number α, there are infinitely many primes p such that ∥αp∥ < p−1/3+ε. Here ∥y∥ denotes the distance from y to the nearest integer. The proof uses Harman's sieve method with arithmetical information coming from bounds for averages of Kloosterman sums.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 267 - 283
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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