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Primitive rational points on expanding horocycles in products of the modular surface with the torus

Published online by Cambridge University Press:  04 June 2020

MANFRED EINSIEDLER
Affiliation:
D-Math, ETH Zürich, Rämistrasse 101, CH-8092Zürich, Switzerland email manfred.einsiedler@math.ethz.ch
MANUEL LUETHI
Affiliation:
Department of Mathematics, University of Tel Aviv, 69978Tel-Aviv, Israel email manuelluthi@mail.tau.ac.il
NIMISH A. SHAH
Affiliation:
The Ohio State University, Columbus, OH 43210, USA email shah@math.ohio-state.edu

Abstract

We prove effective equidistribution of primitive rational points and of primitive rational points defined by monomials along long horocycle orbits in products of the torus and the modular surface. This answers a question posed in joint work by the first and the last named author with Shahar Mozes and Uri Shapira. Under certain congruence conditions we prove the joint equidistribution of conjugate rational points in the $2$-torus and the modular surface.

Type
Original Article
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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