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Counting and equidistribution of reciprocal geodesics and dihedral groups

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arxiv 2204.09956 v1 pith:AJ34LXIG submitted 2022-04-21 math.DS math.GTmath.NT

Viveka Erlandsson , Juan Souto This is my paper · ORCID
classification math.DSmath.GTmath.NT
keywords geodesicsreciprocaldihedralgrowthnumberbourgain-kontorovichbundleclasses
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We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL(2,R), generalizing earlier work of Sarnak and Bourgain-Kontorovich on the growth of the number of reciprocal geodesics on the modular surface. We also prove that reciprocal geodesics are equidistributed in the unit tangent bundle.

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  1. Counting Reciprocal Hyperbolic Elements in Hecke Groups

    math.GT 2025-05 conditional novelty 6.0 of 10

    For each Hecke group Z2*Z_k, the number of primitive reciprocal conjugacy classes of word length 2t grows like a constant times the t-th power of the dominant root of an explicit polynomial, and the same growth holds ...

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