Andreas Mountakis

activity

20222026

most citedFinding product sets in some classes of amenable groups

3 citations · 3 across the 5 of their papers we have counts for

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5 papers · 1 filter

math.DS2026

Monochromatic Almost-Pythagorean Quadruples

James Leng, Redmond McNamara, Andreas Mountakis

We prove that for any set $A$ with positive multiplicative upper density, there exist $x$ , $y$ , $z$ and $w$ in $A$ such that $x^{2} + y^{2} w^{2} = z^{2}$ , generalizing a result of Frantzik…

math.DS2025

Recurrence for pretentious systems along generalized Pythagorean triples

Nikos Frantzikinakis, Andreas Mountakis

We establish multiple recurrence results for pretentious measure-preserving multiplicative actions along generalized Pythagorean triples, that is, solutions to the equation $ax^2 +…

math.DS2025

Infinite unrestricted sumsets in subsets of abelian groups with large density

Dimitrios Charamaras, Ioannis Kousek, Andreas Mountakis +1

Let $(G, +)$ be a countable abelian group such that the subgroup ${g + g : g \in G}$ has finite index and the doubling map $g \mapsto g + g$ has finite kernel. We establish lower bo…

math.DS2024★ 3 cited

Finding product sets in some classes of amenable groups

Dimitrios Charamaras, Andreas Mountakis

In 2022, using methods from ergodic theory, Kra, Moreira, Richter, and Robertson resolved a longstanding conjecture of Erdős about sumsets in large subsets of the natural numbers.…

math.DS2022

Distinguishing sets of strong recurrence from van der Corput Sets

Andreas Mountakis

We construct a set of strong recurrence which is not a van der Corput set. This shows that the class of enhanced van der Corput sets is a proper subclass of sets of strong recurren…