4 citations · 10 across the 8 of their papers we have counts for
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Sequences modulo one: convergence of local statistics
Ilya Vinogradov
We survey recent results beyond equidistribution of sequences modulo one. We focus on the sequence of angles in a Euclidean lattice in and on the sequence $\sqrt n\bm…
The two-point correlation function of the fractional parts of \sqrt{n} is Poisson
Daniel El-Baz, Jens Marklof, Ilya Vinogradov
Elkies and McMullen [Duke Math.J.~123 (2004) 95--139] have shown that the gaps between the fractional parts of \sqrt n for n=1,\ldots,N, have a limit distribution as N tends to inf…
The distribution of directions in an affine lattice: two-point correlations and mixed moments
Daniel El-Baz, Jens Marklof, Ilya Vinogradov
We consider an affine Euclidean lattice and record the directions of all lattice vectors of length at most . Strömbergsson and the second author proved in [Annals of Math.~173 (…
Effective bisector estimate with application to Apollonian circle packings
Ilya Vinogradov
Let Γ<\PSL(2,\C) be a geometrically finite non-elementary discrete subgroup, and let its critical exponent δ be greater than 1. We use representation theory of \PSL(2,\C) to prove…
A Generalization of a Result of Hardy and Littlewood
Ilya Vinogradov
In this note we study the growth of \sum_{m=1}^M\frac1{\|mα\|} as a function of M for different classes of α\in[0,1). Hardy and Littlewood showed that for numbers of bounded type,…