On The Spectral Zeta Function For The Noncommutative Harmonic Oscillator

Takashi Ichinose, Masato Wakayama

研究成果: ジャーナルへの寄稿記事

9 引用 (Scopus)

抄録

The spectral zeta function for the so-called noncommutative harmonic oscillator is able to be meromorphically extended to the whole complex plane, having only one simple pole at the same point s = 1 where Riemann's zeta function ζ(s) has, and possesses a trivial zero at each nonpositive even integer. The essential part of its proof is sketched. A new result is also given on the lower and upper bounds of the eigenvalues of the noncommutative harmonic oscillator.

元の言語英語
ページ(範囲)421-432
ページ数12
ジャーナルReports on Mathematical Physics
59
発行部数3
DOI
出版物ステータス出版済み - 6 1 2007

Fingerprint

Spectral Function
Harmonic Oscillator
Riemann zeta function
harmonic oscillators
Argand diagram
integers
Pole
Upper and Lower Bounds
Trivial
eigenvalues
poles
Eigenvalue
Integer
Zero

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

これを引用

On The Spectral Zeta Function For The Noncommutative Harmonic Oscillator. / Ichinose, Takashi; Wakayama, Masato.

:: Reports on Mathematical Physics, 巻 59, 番号 3, 01.06.2007, p. 421-432.

研究成果: ジャーナルへの寄稿記事

@article{4e2b848e52454e7899cac685a22e683d,
title = "On The Spectral Zeta Function For The Noncommutative Harmonic Oscillator",
abstract = "The spectral zeta function for the so-called noncommutative harmonic oscillator is able to be meromorphically extended to the whole complex plane, having only one simple pole at the same point s = 1 where Riemann's zeta function ζ(s) has, and possesses a trivial zero at each nonpositive even integer. The essential part of its proof is sketched. A new result is also given on the lower and upper bounds of the eigenvalues of the noncommutative harmonic oscillator.",
author = "Takashi Ichinose and Masato Wakayama",
year = "2007",
month = "6",
day = "1",
doi = "10.1016/S0034-4877(07)80077-2",
language = "English",
volume = "59",
pages = "421--432",
journal = "Reports on Mathematical Physics",
issn = "0034-4877",
publisher = "Elsevier Limited",
number = "3",

}

TY - JOUR

T1 - On The Spectral Zeta Function For The Noncommutative Harmonic Oscillator

AU - Ichinose, Takashi

AU - Wakayama, Masato

PY - 2007/6/1

Y1 - 2007/6/1

N2 - The spectral zeta function for the so-called noncommutative harmonic oscillator is able to be meromorphically extended to the whole complex plane, having only one simple pole at the same point s = 1 where Riemann's zeta function ζ(s) has, and possesses a trivial zero at each nonpositive even integer. The essential part of its proof is sketched. A new result is also given on the lower and upper bounds of the eigenvalues of the noncommutative harmonic oscillator.

AB - The spectral zeta function for the so-called noncommutative harmonic oscillator is able to be meromorphically extended to the whole complex plane, having only one simple pole at the same point s = 1 where Riemann's zeta function ζ(s) has, and possesses a trivial zero at each nonpositive even integer. The essential part of its proof is sketched. A new result is also given on the lower and upper bounds of the eigenvalues of the noncommutative harmonic oscillator.

UR - http://www.scopus.com/inward/record.url?scp=36648999325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36648999325&partnerID=8YFLogxK

U2 - 10.1016/S0034-4877(07)80077-2

DO - 10.1016/S0034-4877(07)80077-2

M3 - Article

VL - 59

SP - 421

EP - 432

JO - Reports on Mathematical Physics

T2 - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

SN - 0034-4877

IS - 3

ER -