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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: [email protected]
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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.

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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