In mathematics, the critical line theorem tells us that a positive percentage of the nontrivial zeros of the Riemann zeta function lie on the critical line. Following work by G. H. Hardy and J. E. Littlewood showing there was an infinity of zeros on the critical line, the theorem was proven for a small percentage by Atle Selberg. For other meanings of mathematics or math, see mathematics (disambiguation). ... In mathematics, the Riemann zeta-function, named after Bernhard Riemann, is a function of significant importance in number theory, because of its relation to the distribution of prime numbers. ... In mathematics, the Riemann zeta-function, named after Bernhard Riemann, is a function of significant importance in number theory, because of its relation to the distribution of prime numbers. ... In mathematics, the Riemann zeta-function, named after Bernhard Riemann, is a function of significant importance in number theory, because of its relation to the distribution of prime numbers. ... G. H. Hardy Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ... John Edensor Littlewood (June 9, 1885 - September 6, 1977) was a British mathematician. ... Atle Selberg (born June 17, 1917) is a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory. ...

Norman Levinson improved this to one-third of the zeros^[1], and Conrey^[2] to two-fifths. The Riemann hypothesis implies that the true value would be one. However, if the true value is one, the Riemann hypothesis is not necessarily implied, because if the zeros not on the critical line are only finite in number or infinite but with decreasing frequency, then they can comprise a set of measure zero of all the zeros within the critical strip. Norman Levinson (August 11, 1912 - October 10, 1975) was an American mathematician. ... Unsolved problems in mathematics: Is the real part of a non-trivial zero of the Riemann zeta function always ½?   In mathematics, the Riemann hypothesis (also called the Riemann zeta-hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous unsolved problems. ... In mathematics, the Riemann zeta-function, named after Bernhard Riemann, is a function of significant importance in number theory, because of its relation to the distribution of prime numbers. ...

References

1. ^ Levinson, N., More than one-third of the zeros of Riemann's zeta function are on , Adv. in Math. 13 (1974), 383-436
2. ^ Conrey, J. B., More than two fifths of the zeros of the Riemann zeta function are on the critical line, J. reine angew. Math. 399 (1989), 1-16