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The variance of arithmetic measures associated to closed geodesics on the modular surface
1. | Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH 43210-1174, United States |
2. | Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel and School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, United States |
3. | Department of Mathematics, Princeton University, Fine Hall,Washington Road, Princeton, NJ 08544 and School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, United States |
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Alex Eskin, Maryam Mirzakhani. Counting closed geodesics in moduli space. Journal of Modern Dynamics, 2011, 5 (1) : 71-105. doi: 10.3934/jmd.2011.5.71 |
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Chad Schoen. An arithmetic ball quotient surface whose Albanese variety is not of CM type. Electronic Research Announcements, 2014, 21: 132-136. doi: 10.3934/era.2014.21.132 |
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Artur O. Lopes, Rafael O. Ruggiero. Large deviations and Aubry-Mather measures supported in nonhyperbolic closed geodesics. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1155-1174. doi: 10.3934/dcds.2011.29.1155 |
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Feng Luo. On non-separating simple closed curves in a compact surface. Electronic Research Announcements, 1995, 1: 18-25. |
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Miroslav KolÁŘ, Michal BeneŠ, Daniel ŠevČoviČ. Area preserving geodesic curvature driven flow of closed curves on a surface. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3671-3689. doi: 10.3934/dcdsb.2017148 |
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Bennett Palmer. Stable closed equilibria for anisotropic surface energies: Surfaces with edges. Journal of Geometric Mechanics, 2012, 4 (1) : 89-97. doi: 10.3934/jgm.2012.4.89 |
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Hui Liu, Yiming Long, Yuming Xiao. The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3803-3829. doi: 10.3934/dcds.2018165 |
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Francisco Arana-Herrera. Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani's asymptotics for simple closed hyperbolic geodesics. Journal of Modern Dynamics, 2020, 16: 81-107. doi: 10.3934/jmd.2020004 |
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Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237-244. doi: 10.3934/amc.2017015 |
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Tanja Eisner, Rainer Nagel. Arithmetic progressions -- an operator theoretic view. Discrete and Continuous Dynamical Systems - S, 2013, 6 (3) : 657-667. doi: 10.3934/dcdss.2013.6.657 |
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Mehdi Pourbarat. On the arithmetic difference of middle Cantor sets. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4259-4278. doi: 10.3934/dcds.2018186 |
[12] |
Manish K. Gupta, Chinnappillai Durairajan. On the covering radius of some modular codes. Advances in Mathematics of Communications, 2014, 8 (2) : 129-137. doi: 10.3934/amc.2014.8.129 |
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Margarida Camarinha, Fátima Silva Leite, Peter Crouch. Riemannian cubics close to geodesics at the boundaries. Journal of Geometric Mechanics, 2022 doi: 10.3934/jgm.2022003 |
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Vladimir Dragović, Milena Radnović. Pseudo-integrable billiards and arithmetic dynamics. Journal of Modern Dynamics, 2014, 8 (1) : 109-132. doi: 10.3934/jmd.2014.8.109 |
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Gerhard Frey. Relations between arithmetic geometry and public key cryptography. Advances in Mathematics of Communications, 2010, 4 (2) : 281-305. doi: 10.3934/amc.2010.4.281 |
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Dubi Kelmer. Quadratic irrationals and linking numbers of modular knots. Journal of Modern Dynamics, 2012, 6 (4) : 539-561. doi: 10.3934/jmd.2012.6.539 |
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Robert L. Griess Jr., Ching Hung Lam. Groups of Lie type, vertex algebras, and modular moonshine. Electronic Research Announcements, 2014, 21: 167-176. doi: 10.3934/era.2014.21.167 |
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Jingzhen Liu, Ka Fai Cedric Yiu, Alain Bensoussan. The optimal mean variance problem with inflation. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 185-203. doi: 10.3934/dcdsb.2016.21.185 |
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Igor E. Shparlinski. Close values of shifted modular inversions and the decisional modular inversion hidden number problem. Advances in Mathematics of Communications, 2015, 9 (2) : 169-176. doi: 10.3934/amc.2015.9.169 |
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Alexander Nabutovsky and Regina Rotman. Lengths of geodesics between two points on a Riemannian manifold. Electronic Research Announcements, 2007, 13: 13-20. |
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