We prove that for certain sequences of hyperbolic three--manifolds with cusps which converge to hyperbolic three--space in a weak ("Benjamini-Schramm") sense and certain coefficient systems the regularized analytic torsion approximates the $L^2$-torsion of the universal cover under an additional hypothesis. We also prove an asymptotic equality between the former and some Reidemeister torsion of the truncated manifolds.

中文翻译：

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双曲三流形解析扭转的渐近性

我们证明，对于弱（“Benjamini-Schramm”）意义和某些系数系统的双曲三元流形的某些序列 - 尖点收敛到双曲三元 - 空间和某些系数系统，正则化解析扭转近似于$L^2$-torsion在附加假设下的普遍覆盖。我们还证明了截断流形的前者和某些 Reidemeister 扭之间的渐近等式。