论文标题
在半砷的riemann表面上封闭的大地测量学
Closed geodesics on semi-arithmetic Riemann surfaces
论文作者
论文摘要
在本文中，我们通过数字理论和双曲几何形状研究了半弧度riemann表面的几何方面。首先，我们表明了各种形状的许多半砷的riemann表面的存在，并证明它们的收缩在积极的实际数字中是密集的。此外，这导致了每个属$ g \ geq 2的构造，这是半弧形表面的$ $ geq，具有成对的不同不变的痕迹田地，对B. jeon的猜想产生了负面的答案。最后，对于任何半砷表面，我们都会发现一系列具有对数收缩期生长的一致性覆盖率，并且对于承认模块化嵌入的特殊情况，我们可以表现出明确的常数。
In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove that their systoles are dense in the positive real numbers. Furthermore, this leads to a construction, for each genus $g \geq 2,$ of infinite families of semi-arithmetic surfaces with pairwise distinct invariant trace fields, giving a negative answer to a conjecture of B. Jeon. Finally, for any semi-arithmetic surface we find a sequence of congruence coverings with logarithmic systolic growth and, for the special case of surfaces admitting modular embedding, we are able to exhibit explicit constants.
