Product sets cannot contain long arithmetic progressions
Artikel i vetenskaplig tidskrift, 2014

Let B be a set of real numbers of size n . We prove that the length of the longest arithmetic progression contained in the product set B.B={bibj|bi,bj∈B}B.B={bibj|bi,bj∈B} cannot be greater than View the MathML sourceO(n1+1/loglogn) an arithmetic progression of length View the MathML sourceΩ(nlogn), so the obtained upper bound is close to the optimal.

arithmetic progressions

product sets

convex sets

Författare

Dmitrii Zhelezov

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Acta Arithmetica

0065-1036 (ISSN)

Vol. 163 4 299-307

Fundament

Grundläggande vetenskaper

Ämneskategorier

Diskret matematik

DOI

10.4064/aa163-4-1

Mer information

Skapat

2017-10-07