
Moments for primes in arithmetic progressions, II
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.
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Work Title | Moments for primes in arithmetic progressions, II |
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License | In Copyright (Rights Reserved) |
Work Type | Article |
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Publication Date | November 1, 2003 |
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Deposited | November 17, 2021 |
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