Joel Moreira

activity

20132026

most citedA proof of a sumset conjecture of Erdős

32 citations · 131 across the 20 of their papers we have counts for

collaborators

24 papers

math.DS2026

A short proof of Erdős's $B + C$ 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…

math.DS2025

The Density Finite Sums Theorem

Bryna Kra, Joel Moreira, Florian K. Richter +1

For any set $A$ of natural numbers with positive upper Banach density and any $k \geq 1$ , we show the existence of an infinite set $B \subset N$ and a shift $t \geq 0$ such th…

math.CO2023★ 3 cited

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…

math.DS2022

A proof of Erdős's $B + B + t$ conjecture

Bryna Kra, Joel Moreira, Florian K. Richter +1

We show that every set $A$ of natural numbers with positive upper density can be shifted to contain the restricted sumset ${b_{1} + b_{2} : b_{1}, b_{2} \in B and b_{1} \neq = b_{2}}$ …

math.DS2022★ 12 cited

Infinite Sumsets in Sets with Positive Density

Bryna Kra, Joel Moreira, Florian K. Richter +1

Motivated by questions asked by Erdos, we prove that any set $A \subset N$ with positive upper density contains, for any $k \in N$ , a sumset $B_{1} + \dots + B_{k}$ , where…

math.CO2021★ 1 cited

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 $lo g r / lo g s$ is irrational and $X$ and $Y$ are $\times r$ -…

math.DS2021

Additive averages of multiplicative correlation sequences and applications

Sebastián Donoso, Anh N. Le, Joel Moreira +1

We study sets of recurrence, in both measurable and topological settings, for actions of $(N, \times)$ and $(Q^{> 0}, \times)$ . In particular, we show that autocorre…

math.NT2020★ 5 cited

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…

math.DS2020★ 8 cited

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…

math.DS2020★ 2 cited

Structure of multicorrelation sequences with integer part polynomial iterates along primes

Andreas Koutsogiannis, Anh N. Le, Joel Moreira +1

Let $T$ be a measure preserving $Z^{ℓ}$ -action on the probability space $(X, B, μ),$ $q_{1}, \dots, q_{m} : R \to R^{ℓ}$ vector polynomials, and $f_0,…

math.DS2020★ 2 cited

A decomposition of multicorrelation sequences for commuting transformations along primes

Anh N. Le, Joel Moreira, Florian K. Richter

We study multicorrelation sequences arising from systems with commuting transformations. Our main result is a refinement of a decomposition result of Frantzikinakis and it states t…

math.CO2019★ 11 cited

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…

math.DS2018

Optimal lower bounds for multiple recurrence

Sebastián Donoso, Anh N. Le, Joel Moreira +1

Let $(X, B, μ, T)$ be an ergodic measure preserving system, $A \in B$ and $ε > 0$ . We study the largeness of sets of the form \begin{equation*} \begin{split} S = \l…

math.CO2018★ 32 cited

A proof of a sumset conjecture of Erdős

Joel Moreira, Florian Karl Richter, Donald Robertson

In this paper we show that every set $A \subset N$ with positive density contains $B + C$ for some pair $B, C$ of infinite subsets of $N$ , settling a conjecture of E…

math.DS2017★ 17 cited

Single and multiple recurrence along non-polynomial sequences

Vitaly Bergelson, Joel Moreira, Florian K. Richter

We establish new recurrence and multiple recurrence results for a rather large family $F$ of non-polynomial functions which includes tempered functions defined in [11], a…

math.DS2017★ 4 cited

Disjointness for measurably distal group actions and applications

Joel Moreira, Florian K. Richter, Donald Robertson

We generalize Berg's notion of quasi-disjointness to actions of countable groups and prove that every measurably distal system is quasi-disjoint from every measure preserving syste…

math.DS2016★ 15 cited

A spectral refinement of the Bergelson-Host-Kra decomposition and new multiple ergodic theorems

Joel Moreira, Florian K. Richter

We investigate how spectral properties of a measure preserving system $(X, B, μ, T)$ are reflected in the multiple ergodic averages arising from that system. For certain seq…

math.DS2015

Van der Corput's Difference Theorem: some modern developments

Vitaly Bergelson, Joel Moreira

We discuss various forms of the classical van der Corput's difference theorem and explore applications to and connections with the theory of uniform distribution, ergodic theory, t…

math.DS2015★ 2 cited

Measure preserving actions of affine semigroups and {x+y,xy} patterns

Vitaly Bergelson, Joel Moreira

Ergodic and combinatorial results obtained in [10] involved measure preserving actions of the affine group $A_{K}$ of a countable field $K$ . In this paper we develop a new…

math.CO2015

Large subsets of discrete hypersurfaces in $Z^{d}$ contain arbitrarily many collinear points

Joel Moreira, Florian Karl Richter

In 1977 L.T. Ramsey showed that any sequence in $Z^{2}$ with bounded gaps contains arbitrarily many collinear points. Thereafter, in 1980, C. Pomerance provided a density ve…

math.CO2015

New polynomial and multidimensional extensions of classical partition results

Vitaly Bergelson, John H. Johnson, Joel Moreira

In the 1970s Deuber introduced the notion of $(m, p, c)$ -sets in $N$ and showed that these sets are partition regular and contain all linear partition regular configurations…

math.FA2014

A conditional construction of restricted isometries

Afonso S. Bandeira, Dustin G. Mixon, Joel Moreira

We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an $ε > 0$ su…

math.CO2014

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…

math.CO2013★ 17 cited

Ergodic Theorem involving additive and multiplicative groups of a field and ${x + y, x y}$ patterns

Vitaly Bergelson, Joel Moreira

We establish a "diagonal" ergodic theorem involving the additive and multiplicative groups of a countable field $K$ and, with the help of a new variant of Furstenberg's corresponde…

A short proof of Erdős's B+C conjecture

The Density Finite Sums Theorem

Problems on infinite sumset configurations in the integers and beyond

A proof of Erdős's B+B+t conjecture

Infinite Sumsets in Sets with Positive Density

A combinatorial proof of a sumset conjecture of Furstenberg

Additive averages of multiplicative correlation sequences and applications

Additive and geometric transversality of fractal sets in the integers

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Structure of multicorrelation sequences with integer part polynomial iterates along primes

A decomposition of multicorrelation sequences for commuting transformations along primes

On Rado conditions for nonlinear Diophantine equations

Optimal lower bounds for multiple recurrence

A proof of a sumset conjecture of Erdős

Single and multiple recurrence along non-polynomial sequences

Disjointness for measurably distal group actions and applications

A spectral refinement of the Bergelson-Host-Kra decomposition and new multiple ergodic theorems

Van der Corput's Difference Theorem: some modern developments

Measure preserving actions of affine semigroups and {x+y,xy} patterns

Large subsets of discrete hypersurfaces in Zd contain arbitrarily many collinear points

New polynomial and multidimensional extensions of classical partition results

A conditional construction of restricted isometries

Derandomizing restricted isometries via the Legendre symbol

Ergodic Theorem involving additive and multiplicative groups of a field and {x+y,xy} patterns

A short proof of Erdős's $B + C$ conjecture

A proof of Erdős's $B + B + t$ conjecture

Large subsets of discrete hypersurfaces in $Z^{d}$ contain arbitrarily many collinear points

Ergodic Theorem involving additive and multiplicative groups of a field and ${x + y, x y}$ patterns