81 citations · 223 across the 53 of their papers we have counts for
23 papers · 1 filter
Extreme value laws for intrinsic Diophantine approximation on spheres
Alexander Gorodnik, Zouhair Ouaggag
We study intrinsic Diophantine approximation on the sphere , measured by the quality of the best rational approximation available at a given height. We show that, for $d\geq 3…
Automorphic density estimates and optimal Diophantine exponents
Mikolaj Fraczyk, Alexander Gorodnik, Amos Nevo
The present paper is devoted to establishing an optimal approximation exponent for the action of an irreducible uniform lattice subgroup of a product group on its proper factors. P…
A uniform metrical theorem in multiplicative Diophantine approximation
Michael Björklund, Reynold Fregoli, Alexander Gorodnik
For Lebesgue generic , we investigate the distribution of small values of products with , where $\|\cdot…
On discrepancy, intrinsic Diophantine approximation, and spectral gaps
Alexander Gorodnik, Amos Nevo
In the present paper we establish bounds for the size of the spectral gap for actions of algebraic groups on certain homogeneous spaces. Our approach is based on estimating operato…
Poisson approximation and Weibull asymptotics in the geometry of numbers
Michael Björklund, Alexander Gorodnik
Minkowski's First Theorem and Dirichlet's Approximation Theorem provide upper bounds on certain minima taken over lattice points contained in domains of Euclidean spaces. We study…
Discrepancy of rational points in simple algebraic groups
Alexander Gorodnik, Amos Nevo
The present paper analyzes the discrepancy of distribution of rational points on general semisimple algebraic group varieties. The results include mean-square, almost sure, and uni…