Euler Products Beyond the Boundary

Taro Kimura, Shin ya Koyama, Nobushige Kurokawa

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalLetters in Mathematical Physics
Volume104
Issue number1
DOIs
Publication statusPublished - 2014 Jan
Externally publishedYes

Fingerprint

Euler Product
Riemann hypothesis
Dirichlet L-function
Function Fields
products
Statistical Mechanics
Riemann zeta function
Analogue
statistical mechanics
Line
Zero
analogs
Interpretation

Keywords

  • 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

Cite this

Euler Products Beyond the Boundary. / Kimura, Taro; Koyama, Shin ya; Kurokawa, Nobushige.

In: Letters in Mathematical Physics, Vol. 104, No. 1, 01.2014, p. 1-19.

Research output: Contribution to journalArticle

Kimura, T, Koyama, SY & Kurokawa, N 2014, 'Euler Products Beyond the Boundary', Letters in Mathematical Physics, vol. 104, no. 1, pp. 1-19. https://doi.org/10.1007/s11005-013-0644-3
Kimura, Taro ; Koyama, Shin ya ; Kurokawa, Nobushige. / Euler Products Beyond the Boundary. In: Letters in Mathematical Physics. 2014 ; Vol. 104, No. 1. pp. 1-19.
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