# A logarithmic improvement in the Bombieri–Vinogradov theorem

@article{Sedunova2019ALI, title={A logarithmic improvement in the Bombieri–Vinogradov theorem}, author={Alisa Sedunova}, journal={Journal de Th{\'e}orie des Nombres de Bordeaux}, year={2019} }

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.

## 2 Citations

Optimality for the two-parameter quadratic sieve

- MathematicsActa Arithmetica
- 2022

We study the two-parameter quadratic sieve for a general test function. We prove, under some very general assumptions, that the function considered by Barban and Vehov [BV68] and Graham [Gra78] for…

On a basic mean value theorem with explicit exponents

- MathematicsInternational Journal of Number Theory
- 2021

We follow a paper by Sedunova regarding Vaughan’s basic mean value Theorem to improve and complete a more general demonstration for a suitable class of arithmetic functions as started by Cojocaru and…

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