Rencontres de théorie analytique des nombres

A proof of the Erdős primitive set conjecture

by Jared Duker Lichtman (University of Oxford)

Salle 201, IHP, Paris

Salle 201, IHP, Paris


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

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