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Effective equidistribution of primitive rational points on expanding horospheres
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
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.Comment: 21 pages, incorporates the referee's comments and correction
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