On the spectral zeta function for the noncommutative harmonic oscillator

被引：11

作者：

Ichinose, Takashi ^{[1
]}

Wakayama, Masato

机构：

[1] Kanazawa Univ, Fac Sci, Dept Math, Kanazawa, Ishikawa 9201192, Japan

[2] Kyushu Univ, Fac Math, Fukuoka 8128581, Japan

来源：

REPORTS ON MATHEMATICAL PHYSICS | 2007年 / 59卷 / 03期

基金：

日本学术振兴会;

关键词：

spectral zeta functions; Riemann's zeta function; harmonic oscillator; noncommutative; harmonic oscillators; Weyl's law; Bernoulli's number;

D O I：

10.1016/S0034-4877(07)80077-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 (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.

引用

页码：421 / 432

页数：12

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