Effective joint equidistribution of primitive rational points on expanding horospheres

M Lee, Daniel El-Baz, Bingrong Huang

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

We prove an effective version of a result due to Einsiedler, Mozes, Shah and Shapira who established the equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices in at least 3 dimensions. Their proof uses techniques from homogeneous dynamics and relies in particular on measure-classification theorems -- an approach which does not lend itself to effective bounds. We implement a strategy based on spectral theory, Fourier analysis and Weil's bound for Kloosterman sums in order to quantify the rate of equidistribution for a specific horospherical subgroup in any dimension. We apply our result to provide a rate of convergence to the limiting distribution for the appropriately rescaled diameters of random circulant graphs.
Original languageEnglish
Number of pages21
JournalJournal of the European Mathematical Society
Publication statusAccepted/In press - 12 Apr 2021

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