Joint equidistribution on the product of the circle and the unit cotangent 
bundle of the modular surface

Jana, Subhajit

doi:10.1016/j.jnt.2021.03.010

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Joint equidistribution on the product of the circle and the unit cotangent bundle of the modular surface

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Jana, Subhajit
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.jnt.2021.03.010
(Publisher version)

https://doi.org/10.48550/arXiv.2104.07640
(Preprint)

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Citation

Jana, S. (2021). Joint equidistribution on the product of the circle and the unit cotangent bundle of the modular surface. Journal of Number Theory, 226, 271-283. doi:10.1016/j.jnt.2021.03.010.

Cite as: https://hdl.handle.net/21.11116/0000-0008-C21A-0

Abstract

We use spectral method to prove a joint equidistribution of primitive rational points and the same along expanding horocycle orbits in the products of the circle and the unit cotangent bundle of the modular surface. This result explicates the error bound in a recent work of Einsiedler, Luethi, and Shah [3, Theorem 1.1]. The error is sharp upon the best known progress towards the Ramanujan conjecture at the finite places for the modular surface.