The distribution of a p modulo one

• Autores: Kaisa Matomäki
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 147, Nº 2, 2009, págs. 267-283
• Idioma: inglés
• DOI: 10.1017/s030500410900245x
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• Resumen

  • We prove that, for any irrational number a, there are infinitely many primes p such that ap < p-1/3+e. 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.