论文标题
地球流动的动力学Zeta功能和Fuchsian群体的高维再经扭转
Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups
论文作者
论文摘要
我们表明，由测量流量定义的ruelle zeta函数的零值与单位切线束的高维reidemister扭转相吻合，这是二维多纤维圆柱上的，并且基本组的非独立表示。我们的证明基于Ruelle Zeta函数的整体表达。该积分表达式来自Selberg Zeta函数的功能方程，用于在PSL（2; R）中具有椭圆形元素的离散亚组。我们还表明，较高维度的扭转的渐近行为取决于身份元素对ruelle zeta函数积分表达的贡献。
We show that the absolute value at zero of the Ruelle zeta function defined by the geodesic flow coincides with the higher-dimensional Reidemeister torsion for the unit tangent bundle over a 2-dimensional hyperbolic orbifold and a non-unitary representation of the fundamental group. Our proof is based on the integral expression of the Ruelle zeta function. This integral expression is derived from the functional equation of the Selberg zeta function for a discrete subgroup with elliptic elements in PSL(2;R). We also show that the asymptotic behavior of the higher-dimensional Reidemeister torsion is determined by the contribution of the identity element to the integral expression of the Ruelle zeta function.
