Abstract
The third moment ∑q≤Q ∑a=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 language | English (US) |
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Pages (from-to) | 385-403 |
Number of pages | 19 |
Journal | Duke Mathematical Journal |
Volume | 120 |
Issue number | 2 |
DOIs | |
State | Published - Nov 1 2003 |
All Science Journal Classification (ASJC) codes
- General Mathematics