TY - JOUR
T1 - A proof of a sumset conjecture of Erdős
AU - Robertson, Donald
AU - Moreira, Joel
AU - Richter, Florian
PY - 2019/3/1
Y1 - 2019/3/1
N2 - In this paper we show that every set A ⊂ ℕ with positive density contains B + C for some pair B, C of infinite subsets of ℕ , settling a conjecture of Erdős. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups.
AB - In this paper we show that every set A ⊂ ℕ with positive density contains B + C for some pair B, C of infinite subsets of ℕ , settling a conjecture of Erdős. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups.
UR - https://www.scopus.com/pages/publications/85064038704
U2 - 10.4007/annals.2019.189.2.4
DO - 10.4007/annals.2019.189.2.4
M3 - Article
SN - 1939-8980
VL - 189
SP - 605
EP - 652
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 2
ER -