Limitations to the equi-distribution of primes I

@article{Friedlander1989LimitationsTT,
  title={Limitations to the equi-distribution of primes I},
  author={John B. Friedlander and Andrew Granville},
  journal={Annals of Mathematics},
  year={1989},
  volume={129},
  pages={363-382}
}
In an earlier paper FG] we showed that the expected asymptotic formula (x; q; a) (x)==(q) does not hold uniformly in the range q < x= log N x, for any xed N > 0. There are several reasons to suspect that the expected asymptotic formula might hold, for large values of q, when a is kept xed. However, by a new construction, we show herein that this fails in the same ranges, for a xed and, indeed, for almost all a satisfying 0 < jaj < x= log N x. 

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