肖玄玄，数学博士（法国洛林大学），副教授，澳门科技大学澳门数学研究中心助理主任。主要研究数论中的自守L函数及群轨道中的整数分布研究。参与多项国家自然科学基金项目和澳门科技发展基金项目，发表学术论文十余篇。

AN ASYMPTOTIC LOCAL-GLOBAL THEOREM ON THINSUBGROUPS OF BIANCHI GROUPSXIAO XUANXUAN

Abstract: Bourgain, Gamburd and Sarnak initiated an influential program of studying integers from thin matrix group orbits. This program links to several remarkable applications, such as curvature problems of the Apollonian circle packings, Zaremba’s conjecture, and low-lying fundamental geodesics in the modular surface. In this work we investigate the inverse altitudes of point orbits of thin subgroups of Bianchi groups in and prove an asymptotic local-global theorem.

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