论文标题
计数六氧化双曲线3-纤维数的塞勒姆数量
Counting Salem numbers of arithmetic hyperbolic 3-orbifolds
论文作者
论文摘要
众所周知，算术双曲孔的封闭地球学的长度与塞勒姆数字有关。我们开始对该现象的定量研究。我们表明，任何非紧凑型算术$ 3 $ dimensional orbifold定义$ c q^{1/2} + o（q^{1/4}）$ square-rootable salem salem saleem $ 4 $ $ 4 $，小于或等于$ q $。可以将此数量与此类塞勒姆数字的总数进行比较，该数量被证明是渐近的，与$ \ frac {4} {3} Q^{3/2}+O（q）$。假设Marklof的间隙猜想，我们可以扩展这些结果以紧凑算术$ 3 $ -Orbifolds。作为一种应用，我们获得了在非紧凑型算术算术算术的地球谱中平均多重性的强级增长的下限。以前，此类低界限仅在尺寸$ 2 $和$ 3 $中获得。
It is known that the lengths of closed geodesics of an arithmetic hyperbolic orbifold are related to Salem numbers. We initiate a quantitative study of this phenomenon. We show that any non-compact arithmetic $3$-dimensional orbifold defines $c Q^{1/2} + O(Q^{1/4})$ square-rootable Salem numbers of degree $4$ which are less than or equal to $Q$. This quantity can be compared to the total number of such Salem numbers, which is shown to be asymptotic to $\frac{4}{3}Q^{3/2}+O(Q)$. Assuming the gap conjecture of Marklof, we can extend these results to compact arithmetic $3$-orbifolds. As an application, we obtain lower bounds for the strong exponential growth of mean multiplicities in the geodesic spectrum of non-compact even dimensional arithmetic orbifolds. Previously, such lower bounds had only been obtained in dimensions $2$ and $3$.
