Counting and Equidistribution of Reciprocal Geodesics and Dihedral Groups

Viveka  Erlandsson; Juan  Souto

doi:10.1093/imrn/rnad156

Counting and Equidistribution of Reciprocal Geodesics and Dihedral Groups

Viveka Erlandsson, Juan Souto^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

1 Citation (Scopus)

Abstract

We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL₂R⁠, generalizing the 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.

Original language	English
Article number	rnad156
Pages (from-to)	10298-10318
Number of pages	21
Journal	International Mathematics Research Notices
Volume	2024
Issue number	13
Early online date	25 Apr 2024
DOIs	https://doi.org/10.1093/imrn/rnad156
Publication status	Published - 1 Jul 2024

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© 2024 The Author(s). Published by Oxford University Press.

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abstract = "We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL2R⁠, generalizing the 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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AU - Souto, Juan

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N2 - We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL2R⁠, generalizing the 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.

AB - We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL2R⁠, generalizing the 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.

U2 - 10.1093/imrn/rnad156

DO - 10.1093/imrn/rnad156

M3 - Article (Academic Journal)

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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ER -

Counting and Equidistribution of Reciprocal Geodesics and Dihedral Groups

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