Pair correlation of zeros of the zeta function.

  title={Pair correlation of zeros of the zeta function.},
  author={Patrick X. Gallagher},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={72 - 86}
  • P. Gallagher
  • Published 1985
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
s T— »oo and U-+Q in such a way that UL = A; here L = ̂ —logT is the average 2n density of zeros up to T and A is an arbitrary positive constant. If the same number of points were distributed at random (uniformly and independently on an interval of length Γ), then the ratio on the left would tend to A. According to the conjecture, the zeros have on the average fewer near neighbors than they would have if they were distributed at random. This feature is most striking for small A. 
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