Determinants of Laplacians, the Ray–Singer torsion on lens spaces and the Riemann zeta function
Determinants of Laplacians, the Ray–Singer torsion on lens spaces and the Riemann zeta function
复制标题
拉普拉斯算子的行列式、透镜空间上的 Ray-Singer 挠率和黎曼 zeta 函数
DOI：
10.1063/1.531134
复制
发表时间：
1992
影响因子：
1.3
通讯作者：
D. O. Connor
中科院分区：
文献类型：
--
作者：
C. Nash;D. O. Connor
得到了无限类三维透镜空间L（p,q）的零型和一型拉普拉斯行列式的显式表达式。这些表达式可以组合起来得到这些透镜空间的Ray-Singer扭转。结果得到了黎曼ζ函数ζ(3)的无穷类公式。这些决定因素（和扭转）的值随着透镜空间基本群的大小增加而增长，这也是计算出来的。还注意到仅三个透镜空间L(6,1)， L（10,3）和L（12,5）的扭转的琐碎性。
Explicit expressions are obtained for the determinants of the Laplacians on zero‐ and one‐forms for an infinite class of three dimensional lens spaces L(p,q). These expressions can be combined to obtain the Ray–Singer torsion of these lens spaces. As a consequence an infinite class of formulas is obtained for the Riemann zeta function ζ(3). The value of these determinants (and the torsion) grows as the size of the fundamental group of the lens space increases and this is also computed. The triviality of the torsion for just the three lens spaces L(6,1), L(10,3), and L(12,5) is also noted.