论文标题
算术孔的长度光谱的底部
Bottom of the Length Spectrum of Arithmetic Orbifolds
论文作者
论文摘要
我们证明，当且仅当Salem数字从$ 1 $中统一时，COCOCOCOCTACT算术晶格是统一离散的。我们还证明了半圣母谎言组的类似结果。最后，我们通过显示正常常数$δ（x）> 0 $的存在，阐明了算术Orbifold $γ\ backslash x $的长度底部结构的一些启示，以使封闭的地理位置长度短于$δ$的平方必须是$δ$的平方。
We prove that cocompact arithmetic lattices in a simple Lie group are uniformly discrete if and only if the Salem numbers are uniformly bounded away from $1$. We also prove an analogous result for semisimple Lie groups. Finally, we shed some light on the structure of the bottom of the length spectrum of an arithmetic orbifold $Γ\backslash X$ by showing the existence of a positive constant $δ(X)>0$ such that squares of lengths of closed geodesics shorter than $δ$ must be pairwise linearly dependent over $\mathbb Q$.
