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The large values of the Riemann Zeta-function

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  26 February 2010

Kai-Man Tsang
Kai-Man Tsang
Affiliation:
Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong.

Abstract

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Let |θ| < π/2 and . By refining Selberg's method, we study the large values of as t → ∞ For σ close to ½ we obtain Ω+ estimates that are as good as those obtained previously on the Riemann Hypothesis. In particular, we show that

and

Our results supplement those of Montgomery which are good when σ > ½ is fixed.

MSC classification

Secondary: 11M06: $zeta (s)$ and $L(s, chi)$

Information

Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 203 - 214
Copyright
Copyright © University College London 1993

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