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 2022Show all

5 papers · 1 filter

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

On the distribution of partial quotients of reduced fractions with fixed denominator

Christoph Aistleitner, Bence Borda, Manuel Hauke

In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions $a / N$ , where $N$ is fixed and $a$ runs throu…

math.AC2022

A Signature-Based Gröbner Basis Algorithm with Tail-Reduced Reductors (M5GB)

Manuel Hauke, Lukas Lamster, Reinhard Lüftenegger +1

Gröbner bases are an important tool in computational algebra and, especially in cryptography, often serve as a boilerplate for solving systems of polynomial equations. Research reg…

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…