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On the Riemann zeta-function ζ(s)—Gaps between sign changes of S(t)

Published online by Cambridge University Press:  26 February 2010

Julia Mueller
Julia Mueller
Affiliation:
Department of Pure Mathematics, Fordham University, Bronx, NY 10458, U.S.A.
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Extract

Denote by N(t) the number of zeros β + iγ of ζ(s), s = σ + it, with 0 < β < 1 and 0 < γ < t. It is well known that

where

Type
Research Article
Information
Mathematika , Volume 29 , Issue 2 , December 1982 , pp. 264 - 269
Copyright
Copyright © University College London 1982

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References

1.Ghosh, A.. On Riemann's zeta–function–sign changes of S( T). Recent Progress in Analytic Number Theory, Vol. 1, edited by Halberstam, H. and Hooley, C. (Academic Press, 1981), 25–47.Google Scholar
2.Montgomery, H. L.. Extreme values of the Riemann zeta function. Comment. Math. Helvetia, 52 (1977), 511–518.CrossRefGoogle Scholar
3.Selberg, A.. On the remainder in the formula for N(T), the number of zeros of ζ(s) in the strip 0 < t <T Avhandlinger Norske Vid. Akad. Oslo, 1 (1944).Google Scholar