论文标题
关于弗里德的猜想，用于紧凑的双曲线歧管
On Fried's conjecture for compact hyperbolic manifolds
论文作者
论文摘要
Fried的猜想与原点动力学Zeta函数的行为有关。对于紧凑的双曲线歧管，炸事证明，对于基本组的正交无环代表，扭曲的ruelle zeta函数是holomorphic at $ s = 0 $，其值为$ s = 0 $等于雷轴承分析扭转。他还为非无环的正交表示建立了更一般的结果。本文的目的是将Fried的结果扩展到基本组的任意有限维度表示。卡佩尔和米勒引入的复杂值扭转取代了射线手指的分析扭转。
Fried's conjecture is concerned with the behavior of dynamical zeta functions at the origin. For compact hyperbolic manifolds, Fried proved that for an orthogonal acyclic representation of the fundamental group, the twisted Ruelle zeta function is holomorphic at $s=0$ and its value at $s=0$ equals the Ray-Singer analytic torsion. He also established a more general result for orthogonal representations, which are not acyclic. The purpose of the present paper is to extend Fried's result to arbitrary finite dimensional representations of the fundamental group. The Ray-Singer analytic torsion is replaced by the complex-valued torsion introduced by Cappell and Miller.
