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arXiv · 1705.06660

A logarithmic improvement in the Bombieri-Vinogradov theorem

Alisa Sedunova
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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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Alisa Sedunova. 2017-05-18. A logarithmic improvement in the Bombieri-Vinogradov theorem. https://doi.org/10.5802/jtnb.1098

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