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.
|Work Title||Moments for primes in arithmetic progressions, I|
|License||In Copyright (Rights Reserved)|
|Publication Date||November 1, 2003|
|Publisher Identifier (DOI)||
|Deposited||November 17, 2021|
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