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

collaborators

21 papers

math.NT2025

On the behavior of the colored Jones polynomial of the figure-eight knot under modular transformations

Christoph Aistleitner, Manuel Hauke

The colored Jones polynomial $J_{K, N}$ is an important quantum knot invariant in low-dimensional topology. In his seminal paper on quantum modular forms, Zagier predicted the behav…

math.NT2025

The bad and rough rotation is Poissonian

Manuel Hauke

Motivated by the Berry-Tabor Conjecture and the seminal work of Rudnick-Sarnak, the fine-scale properties of sequences $(a_{n} α)_{n \in N} mod 1$ with $(a_n)_{n \in \mathbb…

math.PR2025

Moment generating functions and moderate deviation principles for lacunary trigonometric sums

Christoph Aistleitner, Lorenz Frühwirth, Manuel Hauke +1

In a recent paper, Aistleitner, Gantert, Kabluchko, Prochno and Ramanan studied large deviation principles (LDPs) for lacunary trigonometric sums $\sum_{n = 1}^{N} cos (2 π n_{k} x)$ , whe…

math.PR2025

On a Problem of Kac concerning Anisotropic Lacunary Sums

Lorenz Fruehwirth, Manuel Hauke

Given a lacunary sequence $(n_{k})_{k \in N}$ , arbitrary positive weights $(c_{k})_{k \in N}$ that satisfy a Lindeberg-Feller condition, and a function $f: \mathbb{T}…

math.NT2024

The Duffin-Schaeffer conjecture with a moving target

Manuel Hauke, Felipe A. Ramirez

We prove the inhomogeneous generalization of the Duffin-Schaeffer conjecture in dimension $m \geq 3$ . That is, given $y \in R^{m}$ and $ψ:\mathbb{N}\to\mathbb{R}_{\g…

math.NT2024★ 1 cited

On Inhomogeneous Poissonian Pair Correlations

Manuel Hauke, Agamemnon Zafeiropoulos

We study the notion of inhomogeneous Poissonian pair correlations, proving several properties that show similarities and differences to its homogeneous counterpart. In particular,…

math.NT2024★ 2 cited

The Duffin-Schaeffer Conjecture for multiplicative Diophantine approximation

Lorenz Frühwirth, Manuel Hauke

Given a monotonically decreasing $ψ : N \to [0, \infty)$ , Khintchine's Theorem provides an efficient tool to decide whether, for almost every $α \in R$ , there are in…

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…

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…

math.NT2021

Weak Poissonian Correlations

Manuel Hauke, Agamemnon Zafeiropoulos

We examine a property of sequences called Poissonian pair correlations with parameter $0 ⩽ β ⩽ 1$ (abbreviated as $β$ -PPC). We prove that when $β < 1,$ the property of…

math.NT2021

On extreme values for the Sudler product of quadratic irrationals

Manuel Hauke

Given a real number $α$ and a natural number $N$ , the Sudler product is defined by $P_{N} (α) = \prod_{r = 1}^{N} 2 ∣ sin (π (r α)) ∣ .$ Denoting by $F_{n}$ th…

math.NT2021

Poissonian correlations of higher orders

Manuel Hauke, Agamemnon Zafeiropoulos

We show that any sequence $(x_{n})_{n \in N} \subseteq [0, 1]$ that has Poissonian correlations of $k$ -th order is uniformly distributed, also providing a quantitative descri…