4 papers
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 +…
On multiplicative recurrence along linear patterns
Dimitrios Charamaras, Andreas Mountakis, Konstantinos Tsinas
In a recent article, Donoso, Le, Moreira and Sun studied sets of recurrence for actions of the multiplicative semigroup and provided some sufficient conditio…
Infinite unrestricted sumsets in subsets of abelian groups with large density
Dimitrios Charamaras, Ioannis Kousek, Andreas Mountakis +1
Let be a countable abelian group such that the subgroup has finite index and the doubling map has finite kernel. We establish lower bo…
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 ErdÅs about sumsets in large subsets of the natural numbers.…