THE DISTRIBUTION OF CLOSED GEODESICS ON THE MODULAR SURFACE, AND DUKE'S THEOREM

被引：0

作者：

Einsiedler, Manfred ^{[1
]}

Lindenstrauss, Elon ^{[2
]}

Michel, Philippe ^{[3
]}

Venkatesh, Akshay ^{[4
]}

机构：

[1] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Hebrew Univ Jerusalem, Einstein Inst Math, Edmond J Safra Campus Givat Ram, IL-91904 Jerusalem, Israel

[3] Ecole Polytech Fed Lausanne, SB IMB TAN, CH-1015 Lausanne, Switzerland

[4] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

ENSEIGNEMENT MATHEMATIQUE | 2012年 / 58卷 / 3-4期

基金：

欧洲研究理事会; 美国国家科学基金会;

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an ergodic theoretic proof of a theorem of Duke about equidistribution of closed geodesics on the modular surface. The proof is closely related to the work of Yu. Linnik and B. Skubenko, who in particular proved this equidistribution under an additional congruence assumption on the discriminant. We give a more conceptual treatment using entropy theory, and show how to use positivity of the discriminant as a substitute for Linnik's congruence condition.

引用

页码：249 / 313

页数：65

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