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Letters in Mathematical Physics

, Volume 104, Issue 1, pp 1–19 | Cite as

Euler Products Beyond the Boundary

  • Taro KimuraEmail author
  • Shin-ya Koyama
  • Nobushige Kurokawa
Article

Abstract

We investigate the behavior of the Euler products of the Riemann zeta function and Dirichlet L-functions on the critical line. A refined version of the Riemann hypothesis, which is named “the Deep Riemann Hypothesis”, is examined. We also study various analogs for global function fields. We give an interpretation for the nontrivial zeros from the viewpoint of statistical mechanics.

Mathematics Subject Classification (2000)

11M06 

Keywords

the Riemann zeta function Dirichlet L-functions the Riemann hypothesis the generalized Riemann hypothesis Euler products 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Taro Kimura
    • 1
    Email author
  • Shin-ya Koyama
    • 2
  • Nobushige Kurokawa
    • 3
  1. 1.Mathematical Physics LaboratoryRIKEN Nishina CenterWakoJapan
  2. 2.Department of Biomedical EngineeringToyo UniversityKawagoeJapan
  3. 3.Department of MathematicsTokyo Institute of TechnologyMeguro-kuJapan

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