In [31] we defined a regularized analytic torsion for quotients of the symmetric space $\operatorname{SL}(n,\mathbb{R})/\operatorname{SO}(n)$ by arithmetic lattices. In this paper we study the limiting behavior of the analytic torsion as the lattices run through sequences of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for principal congruence subgroups and strongly acyclic flat bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the $L^{2}$-analytic torsion.

中文翻译：

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对称空间算术商的 -解析扭转的逼近

在[31]中，我们为对称空间的商定义了一个正则化解析扭转$\operatorname{SL}(n,\mathbb{R})/\operatorname{SO}(n)$通过算术格。在本文中，我们研究了解析扭转的极限行为，因为格子穿过固定算术子群的同余子群序列。我们的主要结果表明，对于主同余子群和强无环扁平丛，解析扭转的对数除以子群的指数，收敛于$L^{2}$-解析扭转。