Geodesic
Concentration of closed geodesics in the homology of modular curves
Forum of Mathematics, Sigma, Tome 11 (2023)

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We prove that the homology classes of closed geodesics associated to subgroups of narrow class groups of real quadratic fields concentrate around the Eisenstein line. This fits into the framework of Duke’s Theorem and can be seen as a real quadratic analogue of results of Michel and Liu–Masri–Young on supersingular reduction of CM-elliptic curves. We also study the level aspect, as well as a homological version of the sup norm problem. Finally, we present applications to group theory and modular forms 
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     author = {Asbj{\o}rn Christian Nordentoft},
     title = {Concentration of closed geodesics in the homology of modular curves},
     journal = {Forum of Mathematics, Sigma},
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     year = {2023},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.85/}
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Asbjørn Christian Nordentoft. Concentration of closed geodesics in the homology of modular curves. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.85

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