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