高秩单李群上范数球上格点的计数
Counting lattice points in norm balls on higher rank simple Lie groups
摘要：
我们建立了一个误差估计计数格点的欧氏范数球（与任意不可约线性表示）的实秩至少为2的单李群。我们的方法利用完善的谱估计的基础上存在的普遍点态界的球面函数的团体。我们特别关注的情况下，特殊线性群，我们给出了一个详细的证明误差估计，这构成了第一次改进的最佳电流界杜克大学，鲁德尼克和Sarnak在1991年建立的，在某些情况下，是近两倍的好。
英文摘要：
We establish an error estimate for counting lattice points in Euclidean norm balls (associated to an arbitrary irreducible linear representation) for lattices in simple Lie groups of real rank at least two. Our approach utilizes refined spectral estimates based on the existence of universal pointwise bounds for spherical functions on the groups involved. We focus particularly on the case of the special linear groups where we give a detailed proof of error estimates which constitute the first improvement of the best current bound established by Duke, Rudnick and Sarnak in 1991, and are nearly twice as good in some cases.
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