Product sets cannot contain long arithmetic progressions
Artikel i vetenskaplig tidskrift, 2013

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} cannot be greater than O(n1+1/loglogn) an arithmetic progression of length Ω(nlogn), so the obtained upper bound is close to the optimal.

Convex sets

Product sets

Arithmetic progressions

Författare

Dmitrii Zhelezov

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Electronic Notes in Discrete Mathematics

1571-0653 (ISSN)

Vol. 43 169-170

Ämneskategorier

Matematik

DOI

10.1016/j.endm.2013.07.028