Manuel Hauke

activity

20212025

most citedThe Duffin-Schaeffer Conjecture for multiplicative Diophantine approximation

2 citations · 4 across the 21 of their papers we have counts for

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Showing 2023Show all

6 papers · 1 filter

math.NT2023

On Sequences with Exponentially Distributed Gaps

Christoph Aistleitner, Manuel Hauke, Agamemnon Zafeiropoulos

We disprove a folklore conjecture stating that a sequence in $[0, 1]$ with exponential gap distribution must necessarily be uniformly distributed.

math.NT2023★ 1 cited

Quantitative inhomogeneous Diophantine approximation for systems of linear forms

Manuel Hauke

The inhomogeneous Khintchine-Groshev Theorem is a classical generalization of Khintchine's Theorem in Diophantine approximation, by approximating points in $R^{m}$ by system…

math.NT2023

Hausdorff dimension estimates for Sudler products with positive lower bound

Dmitry Gayfulin, Manuel Hauke

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

math.DS2023

On Birkhoff sums that satisfy no temporal distributional limit theorem for almost every irrational

Lorenz Frühwirth, Manuel Hauke

Dolgpoyat and Sarig showed that for any piecewise smooth function $f : T \to R$ and almost every pair $(α, x_{0}) \in T \times T$ , $S_N(f,α,x_0) :=…

math.NT2023

Limit laws for cotangent and Diophantine sums

Bence Borda, Lorenz Frühwirth, Manuel Hauke

Limit laws for ergodic averages with a power singularity over circle rotations were first proved by Sinai and Ulcigrai, as well as Dolgopyat and Fayad. In this paper, we prove limi…

math.NT2023

On the metric upper density of Birkhoff sums for irrational rotations

Lorenz Frühwirth, Manuel Hauke

This article examines the value distribution of $S_{N} (f, α) := \sum_{n = 1}^{N} f (n α)$ for almost every $α$ where $N \in N$ is ranging over a long interval and $f$ is a $1$ -p…