Euler Products Beyond the Boundary

Taro Kimura, Shin ya Koyama, Nobushige Kurokawa

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalLetters in Mathematical Physics
Issue number1
Publication statusPublished - 2014 Jan
Externally publishedYes



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

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

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