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A logarithmic improvement in the Bombieri-Vinogradov theorem (1705.06660v3)
Published 18 May 2017 in math.NT
Abstract: In this paper we improve the best known to date result of Dress-Iwaniec-Tenenbaum, getting (log x)2 instead of (log x)5/2. We use a weighted form of Vaughan's identity, allowing a smooth truncation inside the procedure, and an estimate due to Barban-Vehov and Graham related to Selberg's sieve. We give effective and non-effective versions of the result.
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