论文标题
关于紧凑型局部对称轨道的分析扭转的完整渐近学
On full asymptotics of analytic torsions for compact locally symmetric orbifolds
论文作者
论文摘要
我们考虑在紧凑的局部对称的轨道上考虑一定的平坦矢量束，并明确评估相关的渐近线射线启动实际分析扭转。基本思想是通过Selberg的痕量公式计算热量轨迹，因此本文的关键点是评估与非平凡椭圆元素相关的轨道积分。为此，我们推断出几何定位公式，以便我们可以将椭圆形轨道积分重写为与该椭圆形元素的中央器相关的某些身份轨道积分的总和。半密布轨道积分的Bismut的显式几何公式在这些计算中起着至关重要的作用。
We consider a certain sequence of flat vector bundles on a compact locally symmetric orbifold, and we evaluate explicitly the associated asymptotic Ray-Singer real analytic torsion. The basic idea is to computing the heat trace via Selberg's trace formula, so that a key point in this paper is to evaluate the orbital integrals associated with nontrivial elliptic elements. For that purpose, we deduce a geometric localization formula, so that we can rewrite an elliptic orbital integral as a sum of certain identity orbital integrals associated with the centralizer of that elliptic element. The explicit geometric formula of Bismut for semisimple orbital integrals plays an essential role in these computations.
