5 papers
A short proof of Erdős's conjecture
Bryna Kra, Joel Moreira, Florian K. Richter +1
We give a short proof of the fact that every set of natural numbers with positive upper Banach density contains the sum of two infinite sets. The approach simplifies earlier existi…
Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
Vitaly Bergelson, Joel Moreira, Florian K. Richter
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectur…
The Density Finite Sums Theorem
Bryna Kra, Joel Moreira, Florian K. Richter +1
For any set of natural numbers with positive upper Banach density and any , we show the existence of an infinite set and a shift such th…
Problems on infinite sumset configurations in the integers and beyond
Bryna Kra, Joel Moreira, Florian K. Richter +1
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Buildi…
Additive and geometric transversality of fractal sets in the integers
Daniel Glasscock, Joel Moreira, Florian K. Richter
By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expans…