Abstract Let (Ω, A, μ) be a probability space. The classical Borel–Cantelli Lemma states that
for any sequence of μ-measurable sets E i (i= 1, 2, 3,…), if the sum of their measures …

We solve the convergence case of the generalized Baker–Schmidt problem for
simultaneous approximation on affine subspaces, under natural diophantine type …

Let ε> 0. We construct an explicit, full-measure set of α∈[0, 1] such that if γ∈ R then, for
almost all β∈[0, 1], if δ∈ R then there are infinitely many integers n⩾ 1 for which n‖ n α …

We determine the generic multiplicative approximation rate on a hypersurface. There are
four regimes, according to convergence or divergence and curved or flat, and we address all …

Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical
vector. We establish a fully inhomogeneous version of Gallagher's theorem, a diophantine …

In this paper, we prove an effective asymptotic equidistribution result for one-parameter
unipotent orbits in $\mathrm {SL}(3,\mathbb {R})/\mathrm {SL}(3,\mathbb {Z}) $. This enables …

Let (an) n∈ N be a lacunary sequence satisfying the Hadamard gap condition. We give
upper bounds for the maximal gap of the set of dilates {an α} n≤ N modulo 1, in terms of N …

arXiv:2412.12070v1 [math.NT] 16 Dec 2024 Page 1 arXiv:2412.12070v1 [math.NT] 16 Dec
2024 SIMULTANEOUS AND MULTIPLICATIVE DIOPHANTINE APPROXIMATION ON …

Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical
vector. We establish a fully-inhomogeneous version of Gallagher's theorem, a diophantine …

The goal of this survey is to discuss the Quantitative non-Divergence estimate on the space
of lattices and present a selection of its applications. The topics covered include extremal …