Bombieri-Vinogradov theorem


The Bombieri-Vinogradov theorem, sometimes called Bombieri’s theorem, states that for a positive real number A, if x12log-AxQx12 then

qQmaxyxmax1aq(a,q)=1|ψ(x;q,a)-xϕ(q)|=O(x12Q(logx)5),

where ϕ(q) is Euler’s totient function and

ψ(x;q,a)=nxnamodqΛ(n),

where Λ(n) is the Mangoldt functionDlmfMathworldPlanetmath.

Title Bombieri-Vinogradov theorem
Canonical name BombieriVinogradovTheorem
Date of creation 2013-03-22 16:25:36
Last modified on 2013-03-22 16:25:36
Owner Mravinci (12996)
Last modified by Mravinci (12996)
Numerical id 4
Author Mravinci (12996)
Entry type Theorem
Classification msc 11A25
Synonym Bombieri’s theorem