A1 Refereed original research article in a scientific journal
The distribution of alpha p modulo one
Authors: Matomaki K
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2009
Journal: Mathematical Proceedings of the Cambridge Philosophical Society
Journal name in source: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Journal acronym: MATH PROC CAMBRIDGE
Volume: 147
First page : 267
Last page: 283
Number of pages: 17
ISSN: 0305-0041
DOI: https://doi.org/10.1017/S030500410900245X
Abstract
We prove that, for any irrational number alpha, there are infinitely many primes p such that ||alpha p|| < p^(-1/3+epsilon). 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.
We prove that, for any irrational number alpha, there are infinitely many primes p such that ||alpha p|| < p^(-1/3+epsilon). 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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