In mathematics, the critical line theorem says that a positive proportion of the nontrivial zeros of the Riemann zeta function lie on the critical line. Following work by and showing there was an infinity of zeros on the critical line, the theorem was proven for a small positive proportion by . improved this to one-third of the zeros, and to two-fifths. The Riemann hypothesis implies that the true value would be one.

References

• • |last=Selberg|first= Atle |title=On the zeros of Riemann's zeta-function. |journal=Skr. Norske Vid. Akad. Oslo I. |year=1942|volume= 10|pages= 59 pp}}