Moments for primes in arithmetic progressions, II

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The third moment ∑q≤Qa=1q (ψ(x; q, a) - ρ (x; q, a))3 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 those obtained by Hooley in the classical case.

Original languageEnglish (US)
Pages (from-to)385-403
Number of pages19
JournalDuke Mathematical Journal
Issue number2
StatePublished - Nov 1 2003

All Science Journal Classification (ASJC) codes

  • General Mathematics


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