A special value of the spectral zeta function of the non-commutative harmonic oscillators

Hiroyuki Ochiai

doi:10.1007/s11139-007-9065-1

A special value of the spectral zeta function of the non-commutative harmonic oscillators

Hiroyuki Ochiai

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

8 Citations (Scopus)

Abstract

The non-commutative harmonic oscillator is a 2×2-system of harmonic oscillators with a non-trivial correlation. We write down explicitly the special value at s=2 of the spectral zeta function of the non-commutative harmonic oscillator in terms of the complete elliptic integral of the first kind, which is a special case of a hypergeometric function.

Original language	English
Pages (from-to)	31-36
Number of pages	6
Journal	Ramanujan Journal
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s11139-007-9065-1
Publication status	Published - Jan 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

10.1007/s11139-007-9065-1

Cite this

@article{599a641ce2ac46f987bb7a4ba536d9df,

title = "A special value of the spectral zeta function of the non-commutative harmonic oscillators",

abstract = "The non-commutative harmonic oscillator is a 2×2-system of harmonic oscillators with a non-trivial correlation. We write down explicitly the special value at s=2 of the spectral zeta function of the non-commutative harmonic oscillator in terms of the complete elliptic integral of the first kind, which is a special case of a hypergeometric function.",

author = "Hiroyuki Ochiai",

note = "Funding Information: The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) 15340005 from the Ministry of Education, Culture, Sports, Science and Technology.",

year = "2008",

month = jan,

doi = "10.1007/s11139-007-9065-1",

language = "English",

volume = "15",

pages = "31--36",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - A special value of the spectral zeta function of the non-commutative harmonic oscillators

AU - Ochiai, Hiroyuki

N1 - Funding Information: The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) 15340005 from the Ministry of Education, Culture, Sports, Science and Technology.

PY - 2008/1

Y1 - 2008/1

N2 - The non-commutative harmonic oscillator is a 2×2-system of harmonic oscillators with a non-trivial correlation. We write down explicitly the special value at s=2 of the spectral zeta function of the non-commutative harmonic oscillator in terms of the complete elliptic integral of the first kind, which is a special case of a hypergeometric function.

AB - The non-commutative harmonic oscillator is a 2×2-system of harmonic oscillators with a non-trivial correlation. We write down explicitly the special value at s=2 of the spectral zeta function of the non-commutative harmonic oscillator in terms of the complete elliptic integral of the first kind, which is a special case of a hypergeometric function.

UR - http://www.scopus.com/inward/record.url?scp=38349001364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349001364&partnerID=8YFLogxK

U2 - 10.1007/s11139-007-9065-1

DO - 10.1007/s11139-007-9065-1

M3 - Article

AN - SCOPUS:38349001364

SN - 1382-4090

VL - 15

SP - 31

EP - 36

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 1

ER -

A special value of the spectral zeta function of the non-commutative harmonic oscillators

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this