双曲晶格中的角：对相关密度
Angles in hyperbolic lattices : The pair correlation density
摘要：
众所周知，作用在双曲$n$ -空间上的格子中的角变得均匀分布。在本文中，我们确定了一个公式的对相关密度的角度在这样的双曲格。使用这个公式，我们确定，除其他事项外，密度函数在小和大变量限制的渐近行为。这将Boca、Pasol、Popa和Zaharescu以及Kelmer和Kontorovich在2维中的早期结果推广到了一般维$n$。我们的证明使用矩阵系数的衰减与一些仔细的估计，并导致有效的结果与明确的利率。
英文摘要：
It is well known that the angles in a lattice acting on hyperbolic $n$-space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior of the density function in both the small and large variable limits. This extends earlier results by Boca, Pasol, Popa and Zaharescu and Kelmer and Kontorovich in dimension 2 to general dimension $n$. Our proofs use the decay of matrix coefficients together with a number of careful estimates, and lead to effective results with explicit rates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
