More than two fifths of the zeros of the Riemann zeta function are on the critical line.

@article{Conrey1989MoreTT,
  title={More than two fifths of the zeros of the Riemann zeta function are on the critical line.},
  author={J. Brian Conrey},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  year={1989},
  volume={1989},
  pages={1 - 26}
}
  • J. Conrey
  • Published 1989
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
In this paper we show that at least 2/5 of the zeros of the Riemann zeta-function are simple and on the critical line. Our method is a refinement of the method Levinson [11] used when he showed that at least 1/3 of the zeros are on the critical line (and are simple, äs observed by Heath-Brown [10] and, independently, by Seiberg). The main new element here is the use of a mollifier of length y=T with = 4/7 — whereas in Levinson's theorem the mollifier has 0 = 1/2 — . The work [6] of Deshouillers… 
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