# 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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## References

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More than one third of the zeros of Riemann's zeta-function are on = 1/2