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A logarithmic improvement in the Bombieri-Vinogradov theorem

Speaker: Alisa Sedunova

Date: Wed, Feb 8, 2023

Location: PIMS, University of Lethbridge

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory

Abstract:

We improve the best known to date result of Dress-Iwaniec-Tenenbaum, getting ($\log
x)^2$ instead of $\left(log x\right)^(5/2)$. 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.

This event is part of the PIMS CRG Group on L-Functions in Analytic Number Theory. More details can be found on the webpage here: https://sites.google.com/view/crgl-functions/crg-weekly-seminar?authuser=0