Replike群伪模性的同余阻塞
Congruence obstructions to pseudomodularity of Fricke groups
摘要：
伪模群是有限余面积非算术富克斯群，其尖点集恰为$\mathbb{P}^1(\mathbb{Q})$。Long和Reid通过考虑群，即，使单尖环面均匀化的那些。本文证明了具有有理尖点的带状群是伪模的当且仅当它的尖点集在$\mathbb{Q}$的有限顶点上稠密。然后我们推出，无穷多个这样的群不是伪模的。
英文摘要：
A pseudomodular group is a finite coarea nonarithmetic Fuchsian group whose cusp set is exactly $\mathbb{P}^1(\mathbb{Q})$. Long and Reid constructed finitely many of these by considering Fricke groups, i.e., those that uniformize one-cusped tori. We prove that a zonal Fricke group with rational cusps is pseudomodular if and only if its cusp set is dense in the finite adeles of $\mathbb{Q}$. We then deduce that infinitely many such Fricke groups are not pseudomodular.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
