The third moment
is investigated with the novel approximation
and it is shown that when , this leads to more precise conclusions than those obtained by Hooley in the classical case.
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