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Introduction

  • André VorosEmail author
Chapter
  • 803 Downloads
Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 8)

Abstract

The non-real zeros of the Riemann zeta function
$$\zeta(s) \stackrel{\rm def}{=}\sum\limits_{k = 1}^{\infty} k^{-s}\qquad({\rm Re} s > 1),$$
(1.1)
called the Riemann zeros and usually denoted ρ, are most elusive quantities. Thus, no individual Riemann zero is analytically known; and the Riemann Hypothesis (RH): Re \({\rm Re} \rho = \frac{1}{2} (\forall\rho)\), has stayed unresolved since 1859 [92].

Keywords

Meromorphic Function Zeta Function Symmetric Function Summation Formula Riemann Zeta Function 
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 2010

Authors and Affiliations

  1. 1.CEA-Saclay Institut de Physique Théorique (IPhT) Orme des MerisiersGif-sur-YvetteFrance

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