A simpler proof of Levinson's theorem
Published online by Cambridge University Press: 24 October 2008
Extract
In this paper we present a proof of the mean-value theorem required by Levinson to show that at least one-third of the zeros of ζ(s) are on the critical line. As in Levinson [3], let
where Χ(s)=ζ(s)/ζ(1−s) is the usual factor from the functional equation, and let
where
and
where
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 385 - 395
- Copyright
- Copyright © Cambridge Philosophical Society 1985
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