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Littlewood’s theorem and Weyl’s method

  • K. Chandrasekharan
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 167)

Abstract

We have proved in Chapter II, Theorem 4, that all the non-real zeros of Riemann’s zeta-function ζ(s) lie in the critical strip 0≤σ≤1, and are symmetrically situated about the lines σ =1/2 and t = 0, where σ = Re s, t = Im s. We shall now prove a theorem of J. E. Littlewood that there exists a positive constant A such that the region
$$ \sigma>1-\frac{{A\log\log(\left|t\right|+ 3)}}{{\log(\left|t\right|+3)}} $$
(1)
is free from any zero of ζ.

Keywords

Dirichlet Series Riemann Hypothesis Arithmetical Function Prime Number Theorem Partial Summation Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • K. Chandrasekharan
    • 1
  1. 1.Eidgenössische Technische Hochschule ZürichDeutschland

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