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

  title={More than two fifths of the zeros of the Riemann zeta function are on the critical line.},
  author={J. B. Conrey},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={1 - 26}
  • J. B. 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… Expand


Deduction of Semi-Optimal Mollifier for Obtaining Lower Bound for N(0)(T) for Riemann's Zeta-Function.
  • N. Levinson
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1975
Zeros of derivatives of Riemann's xi-function of the critical line. II
The zeros of Riemann's zeta-function on the critical line
On the Zeros of Riemann's Zeta‐Function
Power mean values of the Riemann zeta-function
Titchmarsh, The Theory of the Riemann Zeta-Function
  • Second Ed., Oxford 1986. Oklahoma State University,
  • 1988
Simple Zeros of the Riemann Zeta-Function on the Critical Line
More than one third of zeros of Riemann's zeta-function are on σ = 12
Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial.