4 citations · 10 across the 8 of their papers we have counts for
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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…