Jared Duker Lichtman

University of Oxford University of Oxford

A proof of the Erdős primitive set conjecture

Linfoot Number Theory Seminar

27th April 2022, 11:00 am – 12:00 pm
Fry Building, Room 2.04

A set of integers greater than 1 is primitive if no member in the set divides another. Erdős 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 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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