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 onethird of the zeros, and to twofifths. The
Riemann hypothesis implies that the true value would be one.
References

last=Selbergfirst= Atle
title=On the zeros of Riemann's zetafunction.
journal=Skr. Norske Vid. Akad. Oslo I. year=1942volume= 10pages= 59 pp}}