Agamemnon Zafeiropoulos

activity

20172026

most citedMetric results on summatory arithmetic functions on Beatty sets

5 citations · 13 across the 13 of their papers we have counts for

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13 papers · 1 filter

math.NT2026

Circle coverings driven by arithmetic sequences: a percolation approach to Diophantine approximation and fractal intersections

Manuel Hauke, Andrei Shubin, Eduard Stefanescu +1

We study problems on covering $[0, 1)$ by shrinking intervals centered at the points ${q_{n} x}$ , where $(q_{n})_{n \in N}$ is a given real-valued sequence and $x \in [0, 1)$ i…

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.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

Inhomogeneous Kaufman Measures and Diophantine Approximation

Sam Chow, Agamemnon Zafeiropoulos, Evgeniy Zorin

We introduce an inhomogeneous variant of Kaufman's measure, with applications to diophantine approximation. In particular, we make progress towards a problem related to Littlewood'…

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 the order of magnitude of Sudler products II

Sigrid Grepstad, Mario Neumüller, Agamemnon Zafeiropoulos

We study the asymptotic behavior of Sudler products $P_{N} (α) = \prod_{r = 1}^{N} 2∣ sin π r α ∣$ for quadratic irrationals $α \in R$ . In particular, we verify the convergence of ce…

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…

math.NT2021

Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers

Sam Chow, Agamemnon Zafeiropoulos

We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensional set of pairs of badly approximable numbers on a vertical line. We also prove…

math.NT2020★ 1 cited

On the order of magnitude of Sudler products

Christoph Aistleitner, Niclas Technau, Agamemnon Zafeiropoulos

Given an irrational number $α \in (0, 1)$ , the Sudler product is defined by $P_{N} (α) = \prod_{r = 1}^{N} 2∣ sin π r α ∣$ . Answering a question of Grepstad, Kaltenböck and Neumüller we prove a…

math.NT2019★ 5 cited

Metric results on summatory arithmetic functions on Beatty sets

Marc Technau, Agamemnon Zafeiropoulos

Let $f : N \to C$ be an arithmetic function and consider the Beatty set $B (α) = {⌊ n α ⌋ : n \in N}$ associa…

math.NT2019★ 4 cited

Inhomogeneous Diophantine Approximation on $M_{0}$ -sets with restricted denominators

Andrew D. Pollington, Sanju Velani, Agamemnon Zafeiropoulos +1

Let $F \subseteq [0, 1]$ be a set that supports a probability measure $μ$ with the property that $∣ μ (t) ∣ ≪ (lo g ∣ t ∣)^{- A}$ for some constant $A > 0$ . Let $\mathcal{A}=…

math.NT2018

The discrepancy of $(n_{k} x)$ with respect to certain probability measures

Niclas Technau, Agamemnon Zafeiropoulos

Let $(n_{k})_{k = 1}^{\infty}$ be a lacunary sequence of integers. We show that if $μ$ is a probability measure on $[0, 1)$ such that $∣ μ (t) ∣ \leq c ∣ t ∣^{- η}$ , then for $μ$ -almost…

math.NT2018

The Duffin-Schaeffer conjecture with extra divergence

Christoph Aistleitner, Thomas Lachmann, Marc Munsch +2

The Duffin-Schaeffer conjecture is a fundamental unsolved problem in metric number theory. It asserts that for every non-negative function $ψ : N \to R$ fo…

Circle coverings driven by arithmetic sequences: a percolation approach to Diophantine approximation and fractal intersections

On Inhomogeneous Poissonian Pair Correlations

On Sequences with Exponentially Distributed Gaps

Inhomogeneous Kaufman Measures and Diophantine Approximation

Weak Poissonian Correlations

On the order of magnitude of Sudler products II

Poissonian correlations of higher orders

Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers

On the order of magnitude of Sudler products

Metric results on summatory arithmetic functions on Beatty sets

Inhomogeneous Diophantine Approximation on M0​-sets with restricted denominators

The discrepancy of (nk​x) with respect to certain probability measures

The Duffin-Schaeffer conjecture with extra divergence

Inhomogeneous Diophantine Approximation on $M_{0}$ -sets with restricted denominators

The discrepancy of $(n_{k} x)$ with respect to certain probability measures