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arXiv · 2203.06446

Concentration of closed geodesics in the homology of modular curves

Asbjørn Christian Nordentoft
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Abstract

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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Asbjørn Christian Nordentoft. 2022-03-12. Concentration of closed geodesics in the homology of modular curves. https://arxiv.org/abs/2203.06446

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