Mathematische Annalen

, Volume 370, Issue 1–2, pp 381–421 | Cite as

Effective equidistribution of shears and applications

  • Dubi Kelmer
  • Alex KontorovichEmail author


A “shear” is a unipotent translate of a cuspidal geodesic ray in the quotient of the hyperbolic plane by a non-uniform discrete subgroup of \({\text {PSL}}(2,\mathbb {R})\), possibly of infinite co-volume. We prove the regularized equidistribution of shears under large translates with effective (that is, power saving) rates. We also give applications to weighted second moments of GL(2) automorphic L-functions, and to counting lattice points on locally affine symmetric spaces.



The authors would like to express their gratitude to Jens Marklof, Curt McMullen, and Peter Sarnak for many enlightening comments and suggestions. The second author would especially like to thank Valentin Blomer, Farrell Brumley, and Nicolas Templier for many hours of discussion about this problem; see also the related work in [1].


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© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Boston CollegeBostonUSA
  2. 2.Rutgers UniversityNew BrunswickUSA

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