负弯曲局部对称黎曼流形的长度重数分布
Distributions of length multiplicities for negatively curved locally symmetric Riemannian manifolds
摘要：
研究了负曲率局部对称黎曼流形的长度重数分布。在定理2.1中，我们给出了一般（不一定是紧的）情形下长度重数及其平方和的上界。在定理2.2中，我们进一步得到了基本群是模群的同余子群的算术曲面的长度重数及其幂和的更精确的估计。
英文摘要：
The aim of the present paper is to study the distributions of the length multiplicities for negatively curved locally symmetric Riemannian manifolds. In Theorem 2.1, we give upper bounds of the length multiplicities and the square sums of them for general (not necessarily compact) cases. Furthermore in Theorem 2.2, we obtain more precise estimates of the length multiplicities and the power sums of them for arithmetic surfaces whose fundamental groups are congruence subgroups of the modular group.
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