Abstract
We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves.
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Acknowledgement
We would like to thank Edgar Assing, Manfred Einsiedler, Elon Lindenstrauss, Manuel Lüthi, Asbjørn Nordentoft, Dinakar Ramakrishnan, Peter Sarnak and Radu Toma, for very useful conversations and comments. We would like to thank the referees for their very careful reading of the manuscript and for pointing out some inaccuracies in a previous version.
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Dedicated to Peter Sarnak with admiration
First author supported in part by Germany’s Excellence Strategy grant EXC-2047/1 - 390685813 and ERC Advanced Grant 101054336.
Second author partially supported by the SNF grant 200021_197045.
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Blomer, V., Michel, P. The unipotent mixing conjecture. JAMA 151, 25–57 (2023). https://doi.org/10.1007/s11854-023-0326-8
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DOI: https://doi.org/10.1007/s11854-023-0326-8