32 citations · 131 across the 20 of their papers we have counts for
8 papers · 1 filter
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…
A combinatorial proof of a sumset conjecture of Furstenberg
Daniel Glasscock, Joel Moreira, Florian K. Richter
We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if is irrational and and are -…
On Rado conditions for nonlinear Diophantine equations
Jordan Mitchell Barrett, Martino Lupini, Joel Moreira
Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These conditions are inspired…
A proof of a sumset conjecture of Erdős
Joel Moreira, Florian Karl Richter, Donald Robertson
In this paper we show that every set with positive density contains for some pair of infinite subsets of , settling a conjecture of E…
Large subsets of discrete hypersurfaces in contain arbitrarily many collinear points
Joel Moreira, Florian Karl Richter
In 1977 L.T. Ramsey showed that any sequence in with bounded gaps contains arbitrarily many collinear points. Thereafter, in 1980, C. Pomerance provided a density ve…
New polynomial and multidimensional extensions of classical partition results
Vitaly Bergelson, John H. Johnson, Joel Moreira
In the 1970s Deuber introduced the notion of -sets in and showed that these sets are partition regular and contain all linear partition regular configurations…
Derandomizing restricted isometries via the Legendre symbol
Afonso S. Bandeira, Matthew Fickus, Dustin G. Mixon +1
The restricted isometry property (RIP) is an important matrix condition in compressed sensing, but the best matrix constructions to date use randomness. This paper leverages pseudo…
Ergodic Theorem involving additive and multiplicative groups of a field and patterns
Vitaly Bergelson, Joel Moreira
We establish a "diagonal" ergodic theorem involving the additive and multiplicative groups of a countable field and, with the help of a new variant of Furstenberg's corresponde…