Hierarchy of the Selberg Zeta functions

被引：3
作者：
Hashimoto, Y
Wakayama, M
机构：
[1] Kyushu Univ, Grad Sch Math, Fukuoka 8128581, Japan
[2] Kyushu Univ, Fac Math, Fukuoka 8128581, Japan
来源：
LETTERS IN MATHEMATICAL PHYSICS | 2005年 / 73卷 / 01期
关键词：
Selberg's zeta function; functional equation; zeta regularized determinant; Riemann surface; multiple gamma function;
D O I：
10.1007/s11005-005-6784-3
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.
引用
收藏
页码：59 / 70
页数：12
相关论文
共 17 条
[1]  
Barnes E., 1904, T CAMBRIDGE PHILOS S, V19, P374
[2]  
CARTIER P, 1988, CR ACAD SCI I-MATH, V307, P143
[3]   ON DETERMINANTS OF LAPLACIANS ON RIEMANN SURFACES [J].
DHOKER, E ;
PHONG, DH .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 104 (04) :537-545
[4]  
GON Y, 2005, DIRICHLET SERIES CON
[5]  
HEJHAL D, 1976, SPRINGER LEC NOTES M, V548
[6]   Quantum KZ equation with vertical bar q vertical bar=1 and correlation functions of the XXZ model in the gapless regime [J].
Jimbo, M ;
Miwa, T .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (12) :2923-2958
[7]   Remarks on zeta regularized products [J].
Kimoto, K ;
Wakayama, M .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2004, 2004 (17) :855-875
[8]   Higher Selberg zeta functions [J].
Kurokawa, N ;
Wakayama, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 247 (02) :447-466
[9]   Multiple sine functions [J].
Kurokawa, N ;
Koyama, SY .
FORUM MATHEMATICUM, 2003, 15 (06) :839-876
[10]   Casimir effects on Riemann surfaces [J].
Kurokawa, N ;
Wakayama, M .
INDAGATIONES MATHEMATICAE-NEW SERIES, 2002, 13 (01) :63-75
12