We show an equality between the analytic torsion and the absolute value at zero of the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an acyclic flat vector bundle obtained by the restriction of a representation of the underlying Lie group. This generalises author’s previous result for unitarily flat vector bundles, and the results of Bröcker, Müller, and Wotzke on closed hyperbolic manifolds.

中文翻译：

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解析扭力，动态Zeta函数和允许扭曲的Fried猜想

我们显示了解析扭力与闭合奇数维局部对称空间上的Ruelle动力学zeta函数在零处的绝对值之间的相等性，该局部对称空间由无环平面向量束扭曲（通过限制底层Lie基团的表示而获得）。这归纳了作者先前对于单位平面矢量束的结果，以及Bröcker，Müller和Wotzke在闭合双曲流形上的结果。