4 citations · 10 across the 8 of their papers we have counts for
12 papers
Effective equidistribution of horocycle lifts
Ilya Vinogradov
We give a rate of equidistribution of lifts of horocycles from the space to the space $\mathrm{ASL}(2,\mathbb Z)\back…
Central limit theorems for simultaneous Diophantine approximations
Dmitry Dolgopyat, Bassam Fayad, Ilya Vinogradov
We study the distribution modulo of the values taken on the integers of linear forms in variables with random coefficients. We obtain quenched and annealed central limi…
Spherical averages in the space of marked lattices
Jens Marklof, Ilya Vinogradov
A marked lattice is a -dimensional Euclidean lattice, where each lattice point is assigned a mark via a given random field on . We prove that, if the field is str…
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…
Directions in hyperbolic lattices
Jens Marklof, Ilya Vinogradov
It is well known that the orbit of a lattice in hyperbolic -space is uniformly distributed when projected radially onto the unit sphere. In the present work, we consider the fin…
Effective Ratner theorem for ASL(2,R) and gaps in \sqrt{n} modulo 1
Tim Browning, Ilya Vinogradov
Let G=ASL(2,R) be the affine special linear group of the plane, and set Gamma=ASL(2,Z). Building on recent work of Strömbergsson we prove a rate of equidistribution for the orbits…
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 (…
Ergodic Properties of -Free Integers in Number Fields
Francesco Cellarosi, Ilya Vinogradov
Let be a degree extension. Inside the ring of integers we define the set of -free integers and a natural -action on…
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…
Limiting distribution of visits of sereval rotations to shrinking intervals
Ilya Vinogradov
We show that given normalized intervals on the unit circle, the numbers of visits of random rotations to these intervals have a joint limiting distribution as lengths of tr…
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,…