论文标题
复杂的有价值的分析扭转和局部对称空间上的动态Zeta功能
Complex valued analytic torsion and dynamical zeta function on locally symmetric spaces
论文作者
论文摘要
我们表明，在封闭的奇数尺寸局部对称空间上，ruelle动力学Zeta功能由任意的平面矢量束扭曲，其Meromorormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormoright在零点的laurent系列中的领先项与Cappell-Miller平面Laplacian的正则确定性有关。当平坦矢量束接近无环和单一的捆绑包时，我们表明动态Zeta函数在零点是规则的，其值等于Cappell-Miller的复杂有价值的分析扭转。这是作者对单位扁平向量束以及穆勒和Spilioti在双曲歧管上的结果的先前结果。
We show that the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an arbitrary flat vector bundle has a meromorphic extension to the whole complex plane and that its leading term in the Laurent series at the zero point is related to the regularised determinant of the flat Laplacian of Cappell-Miller. When the flat vector bundle is close to an acyclic and unitary one, we show that the dynamical zeta function is regular at the zero point and that its value is equal to the complex valued analytic torsion of Cappell-Miller. This generalises author's previous results for unitarily flat vector bundles as well as Müller and Spilioti's results on hyperbolic manifolds.
