1 November 2003 Moments for primes in arithmetic progressions, II
R. C. Vaughan
Duke Math. J. 120(2): 385-403 (1 November 2003). DOI: 10.1215/S0012-7094-03-12027-X

Abstract

The third moment

q Q a = 1 q ( 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

F R ( n ) = r R μ ( r ) ϕ ( r ) b = 1 ( b , r ) = 1 r e ( b n / r ) ,

and it is shown that when R log A x , this leads to more precise conclusions than those obtained by Hooley in the classical case.

Citation

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R. C. Vaughan. "Moments for primes in arithmetic progressions, II." Duke Math. J. 120 (2) 385 - 403, 1 November 2003. https://doi.org/10.1215/S0012-7094-03-12027-X

Information

Published: 1 November 2003
First available in Project Euclid: 16 April 2004

zbMATH: 1053.11078
MathSciNet: MR2019981
Digital Object Identifier: 10.1215/S0012-7094-03-12027-X

Subjects:
Primary: 11N13

Rights: Copyright © 2003 Duke University Press

Vol.120 • No. 2 • 1 November 2003
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