3 papers
math.NT2026
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…
math.NT2024
Effective estimate and Central Limit Theorem for Diophantine approximation on spheres
Zouhair Ouaggag
We study the counting function of rational approximations with given bounds on the denominator and satisfying the critical Dirichlet exponent on the sphere , . We giv…
math.NT2022
Effective rational approximation on spheres
Zouhair Ouaggag
We prove an effective estimate for the counting function of Diophantine approximants on the sphere S. We use homogeneous dynamics on the space of orthogonal lattices, in partic…