Moments for primes in arithmetic progressions, I

The second moment ∑q≤Q ∑a=1q (ψ(x; q, a) - ρ (x; q, a))2 is investigated with the novel approximation ρ(x; q, a) = ∑n≤x n≡a (mod q) F R(n), where FR(n) = ∑r≤R μ(r)/φ(r) ∑b=1 (b,r)=1r e(bn/r), and it is shown that when R ≤ logA x, this leads to more precise conclusions than in the classical Montgomery-Hooley case.

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Work Title Moments for primes in arithmetic progressions, I
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Open Access
Creators
  1. Robert Charles Vaughan
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Duke Mathematical Journal
Publication Date November 1, 2003
Publisher Identifier (DOI)
  1. https://doi.org/10.1215/S0012-7094-03-12026-8
Deposited November 17, 2021

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