We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal ['On the uniform equidistribution of long closed horocycles', Loo-Keng Hua: a great mathematician of the twentieth century, Asian J. Math. 4 (2000) 839-853] and Str?mbergsson ['On the uniform equidistribution of long closed horocycles', Duke Math. J. 123 (2004) 507-547] in dimension 2. Our proofs use spectral methods, and lead to precise estimates on the rate of convergence to equidistribution.
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机译:我们证明了任意维数的有限双曲流形中大的封闭球面的渐近均衡分布结果。这扩展了Hejhal的早期研究成果[“关于长封闭式摩托车的均匀均等分布”,Loo-Keng Hua:20世纪的杰出数学家,亚洲J.数学。 4(2000)839-853]和Str?mbergsson [“关于长封闭卧式摩托车的均匀分配”,杜克·马特(Duke Math)。 J. 123(2004)507-547]中的维度2。我们的证明使用频谱方法,并导致对收敛到均值分布的速率进行精确估计。
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