模群的组合增长
Combinatorial Growth in the Modular Group
摘要：
我们考虑一个用尽的模块orbifold紧凑的子表面和显示的增长率，在字长，这样的子表面上的倒易测地线（所谓的低洼倒易测地线）收敛到增长率的模块orbifold上的倒易测地线的全套。我们得到了一个类似的结果为低洼测地线和他们的增长率收敛到的增长率的闭测地线的全部集合。
英文摘要：
We consider an exhaustion of the modular orbifold by compact subsurfaces and show that the growth rate, in terms of word length, of the reciprocal geodesics on such subsurfaces (so named low lying reciprocal geodesics) converge to the growth rate of the full set of reciprocal geodesics on the modular orbifold. We derive a similar result for the low lying geodesics and their growth rate convergence to the growth rate of the full set of closed geodesics.
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