Manuel Hauke

collaborators

3 papers

math.NT2022

On the asymptotic behaviour of Sudler products for badly approximable numbers

Manuel Hauke

Given a badly approximable number $α$ , we study the asymptotic behaviour of the Sudler product defined by $P_{N} (α) = \prod_{r = 1}^{N} 2∣ sin π r α ∣$ . We show that $\liminf_{N \to \inf…

math.NT2022

Metric density results for the value distribution of Sudler products

Manuel Hauke

We study the value distribution of the Sudler product $P_{N} (α) := \prod_{n = 1}^{N} ∣ 2 sin (π n α)∣$ for Lebesgue-almost every irrational $α$ . We show that for every non-decrea…

math.NT2022

On the metric theory of approximations by reduced fractions: a quantitative Koukoulopoulos-Maynard theorem

Christoph Aistleitner, Bence Borda, Manuel Hauke

Let $ψ : N \to [0, 1/2]$ be given. The Duffin-Schaeffer conjecture, recently resolved by Koukoulopoulos and Maynard, asserts that for almost all reals $α$ there are infinite…