A proof of the Erdos primitive set conjecture

Abstract: A set of integers greater than 1 is primitive if no member in the set divides another. Erdos proved in 1935 that the series of $1/(n\log n)$, ranging over $n$ in $A$, is uniformly bounded over all choices of primitive sets $A$. In 1988 he asked if this bound is attained for the set of prime numbers. In this talk we describe recent work which answers Erdos' conjecture in the affirmative. We will also discuss applications to old questions of Erdos, Sarkozy, and Szemeredi from the 1960s.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)