Euler Products Beyond the Boundary

Taro Kimura; Shin ya Koyama; Nobushige Kurokawa

doi:10.1007/s11005-013-0644-3

Euler Products Beyond the Boundary

Taro Kimura, Shin ya Koyama, Nobushige Kurokawa

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 language	English
Pages (from-to)	1-19
Number of pages	19
Journal	Letters in Mathematical Physics
Volume	104
Issue number	1
DOIs	https://doi.org/10.1007/s11005-013-0644-3
Publication status	Published - 2014 Jan
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s11005-013-0644-3

Cite this

@article{91e507d5feff45e883910b545e1d91fa,

title = "Euler Products Beyond the Boundary",

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.",

keywords = "Dirichlet L-functions, Euler products, the Riemann hypothesis, the Riemann zeta function, the generalized Riemann hypothesis",

author = "Taro Kimura and Koyama, {Shin ya} and Nobushige Kurokawa",

note = "Funding Information: Taro Kimura: Partially supported by JSPS Research Fellowships for Young Scientists (Nos. 23-593, 25-4302).",

year = "2014",

month = jan,

doi = "10.1007/s11005-013-0644-3",

language = "English",

volume = "104",

pages = "1--19",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Euler Products Beyond the Boundary

AU - Kimura, Taro

AU - Koyama, Shin ya

AU - Kurokawa, Nobushige

N1 - Funding Information: Taro Kimura: Partially supported by JSPS Research Fellowships for Young Scientists (Nos. 23-593, 25-4302).

PY - 2014/1

Y1 - 2014/1

N2 - 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.

AB - 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.

KW - Dirichlet L-functions

KW - Euler products

KW - the Riemann hypothesis

KW - the Riemann zeta function

KW - the generalized Riemann hypothesis

UR - http://www.scopus.com/inward/record.url?scp=84891513893&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84891513893&partnerID=8YFLogxK

U2 - 10.1007/s11005-013-0644-3

DO - 10.1007/s11005-013-0644-3

M3 - Article

AN - SCOPUS:84891513893

SN - 0377-9017

VL - 104

SP - 1

EP - 19

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 1

ER -

Euler Products Beyond the Boundary

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this