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.
"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