Translates of rational points along expanding closed horocycles on the modular surface
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Date
2022-02
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Journal Article
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Abstract
We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface. Using spectral methods we confirm equidistribution of these sample points for any translate when the sequence of horocycles expands within a certain polynomial range. We show that the equidistribution fails for generic translates and a slightly faster expanding rate. We also prove both equidistribution and non-equidistribution results by obtaining explicit limiting measures while allowing the sequence of horocycles to expand arbitrarily fast. Similar results are also obtained for translates of primitive rational points.
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382 (1)
Pages / Article No.
655 - 717
Publisher
Springer
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08802 - Iozzi, Alessandra (Tit.-Prof.)