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
收藏
页码：421 / 432
页数：12
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