We examine the effects of certain hypothetical configurations of zeros of Dirichlet L-functions lying off the critical line on the distribution of primes in arithmetic progressions.
"The prime number race and zeros of L-functions off the critical line." Duke Math. J. 113 (2) 313 - 330, 1 June 2002. https://doi.org/10.1215/S0012-7094-02-11324-6