Closed geodesics on semi-arithmetic Riemann surfaces
Closed geodesics on semi-arithmetic Riemann surfaces
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半算术黎曼曲面上的闭合测地线
DOI：
10.4310/mrl.2022.v29.n4.a3
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发表时间：
2020
影响因子：
1
通讯作者：
Cayo D'oria
中科院分区：
文献类型：
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作者：
Gregory Cosac;Cayo D'oria
本文用数论和双曲几何的方法研究了半算术黎曼曲面的几何性质。首先，我们证明了无穷多个不同形状的半算术Riemann曲面的存在性，并证明了它们的系统是正实数稠密的。此外，对于每个亏格$ggeq2，构造了一个具有两两不变不变迹场的半算术曲面族，从而否定了B.Jeon的一个猜想。最后，对于任何半算术曲面，我们找到了一个具有对数收缩增长的同余覆盖序列，并且，对于允许模嵌入的曲面的特殊情况，我们能够证明显式常数。
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.
DOI：
10.1007/978-4-431-68174-8
发表时间：
1992-07
期刊：
--
影响因子：
--
作者：
M. Taniguchi;M. Taniguchi;Ysoichi Imayoshi;Yôichi Imayoshi
通讯作者：
M. Taniguchi;M. Taniguchi;Ysoichi Imayoshi;Yôichi Imayoshi