A logarithmic improvement in the Bombieri–Vinogradov theorem

  title={A logarithmic improvement in the Bombieri–Vinogradov theorem},
  author={Alisa Sedunova},
  journal={Journal de Th{\'e}orie des Nombres de Bordeaux},
  • A. Sedunova
  • Published 18 May 2017
  • Mathematics
  • Journal de Théorie des Nombres de Bordeaux
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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