论文标题
等分分配和定期扁平托里的计数
Equidistribution and counting of periodic flat tori
论文作者
论文摘要
让$ g $为一个半谎言组，没有紧凑的因素，$γ<g $无扭转，无旋塞，不可减至的晶格。根据Selberg的说法，常规Weyl腔室流的周期性轨道生活在Weyl腔室空间的最大平坦周期性的摩擦上。我们证明，这些固定的周期性摩ri等分呈指数速度，以达到HAAR度量的商。根据等分分配公式，我们得出了更高的排名主要测量定理。这些计数和等分分配结果在非共同的，有限的库伏案例中也得出，用于$ g = \ mathrm {Slrm {sl}（d，d，\ m mathbb {r}）$和$γ<\ mathrm {slrm {Slrm {sl}（d，d，d，d，\ mathbb {z}）$ a FITAILE INDEX INDEX INDEX INDEX INDEX INDEX subgrout。
Let $G$ be a semisimple Lie group without compact factor and $Γ< G$ a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber flows live on maximal flat periodic tori of the space of Weyl chambers. We prove that these flat periodic tori equidistribute exponentially fast towards the quotient of the Haar measure. From the equidistribution formula, we deduce a higher rank prime geodesic theorem. These counting and equidistribution results also hold in the non cocompact, finite covolume case for $G=\mathrm{SL}(d,\mathbb{R})$ and $Γ<\mathrm{SL}(d,\mathbb{Z})$ a finite index subgroup.
