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The variance of closed geodesics in balls and annuli on the modular surface

de Faveri, Alexandre (2022) The variance of closed geodesics in balls and annuli on the modular surface. Advances in Mathematics, 403 . Art. No. 108390. ISSN 0001-8708. doi:10.1016/j.aim.2022.108390. https://resolver.caltech.edu/CaltechAUTHORS:20220511-655901200

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Abstract

We asymptotically estimate the variance for the distribution of closed geodesics in small random balls or annuli on the modular surface Γ\H. A probabilistic model in which closed geodesics are modeled using random geodesic segments is proposed, and we rigorously analyze this model using mixing of the geodesic flow in Γ\H. This leads to a conjecture for the asymptotic behavior of the variance, which unlike in previously explored cases is not equal to the expected value. We prove this conjecture for small balls and annuli, resolving a question left open by Humphries and Radziwiłł.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.aim.2022.108390DOIArticle
https://arxiv.org/abs/2103.06436arXivDiscussion Paper
Additional Information:© 2022 Elsevier Inc. Received 24 March 2021, Revised 13 February 2022, Accepted 28 March 2022, Available online 14 April 2022, Version of Record 14 April 2022.
Subject Keywords:L-function; Geodesic; Geometric invariant
Classification Code:MSC: 11E45; 11F67
DOI:10.1016/j.aim.2022.108390
Record Number:CaltechAUTHORS:20220511-655901200
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220511-655901200
Official Citation:Alexandre de Faveri, The variance of closed geodesics in balls and annuli on the modular surface, Advances in Mathematics, Volume 403, 2022, 108390, ISSN 0001-8708, https://doi.org/10.1016/j.aim.2022.108390.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114681
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 May 2022 21:14
Last Modified:11 May 2022 21:14

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