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math.NT2022
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…
math.NT2022
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…
math.NT2022
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…