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Primitive rational points on expanding horocycles in products of the modular surface with the torus
Part of
MANFRED EINSIEDLER, MANUEL LUETHI, NIMISH A. SHAH
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 6 / June 2021

Published online by Cambridge University Press:

04 June 2020, pp. 1706-1750

Print publication:

June 2021
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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.