Littlewood’s theorem and Weyl’s method

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


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
$$ \sigma>1-\frac{{A\log\log(\left|t\right|+ 3)}}{{\log(\left|t\right|+3)}} $$
is free from any zero of ζ.


Dirichlet Series Riemann Hypothesis Arithmetical Function Prime Number Theorem Partial Summation Formula 
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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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