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Graduate Student Number Theory Learning Seminar

Sets of Large Harmonic Sum Containing no Long Arithmetic Progressions

Alex Walker, Rutgers

Location:  Via Zoom, email Brooke at: bl481@math.rutgers.edu for login information.
Date & time: Wednesday, 16 September 2020 at 1:30PM - 2:30PM

Abstract: How large can the harmonic sum of a set of integers be, when that set includes no arithmetic progression of \(k\) terms? A conjecture of Erdos' posits that these harmonic sums should be finite. If so, how quickly can these sums grow as \(k\) tends to infinity. In this talk, I describe a new construction for \(k\)-term-progression-avoiding sets which is amenable to computer search.  We produce some record-setting sets and are left with a lot more questions.

 

website: https://sites.math.rutgers.edu/~bl481/NumberTheorySeminar.html