Metric uniform distribution on analytic curves

We obtain multidimensional metric uniform distribution results involving sequences in Rᵏ parametrized by analytic curves. Our theorems extend the classical theorems of Weyl and Koksma in a variety of ways. One of our main results implies that for any injective sequences a₁,,aₖ: N→ Z the set \(x₁,,xₖ)∈ Rᵏ:(a₁(n)x₁,,aₖ(n)xₖ)_n∈ N is uniformly distributed in Tᵏ\ has full Lebesgue measure inside any non-degenerate analytic curve γ⊂ Rᵏ.