A logarithmic improvement in the Bombieri-Vinogradov theorem
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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