Improved bounds for arithmetic progressions in product sets
Artikel i vetenskaplig tidskrift, 2015

Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic progression contained in the product set B.B = {bb′|b, b′ ∈ B} cannot be greater than O(n log n) which matches the lower bound provided in an earlier paper up to a multiplicative constant. For sets of complex numbers, we improve the bound to Oϵ(n1 + ϵ) for arbitrary ϵ > 0 assuming the GRH.

prime factors

arithmetic progressions

polynomials

Product sets

Författare

Dmitrii Zhelezov

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

International Journal of Number Theory

1793-0421 (ISSN)

Vol. 11 8 2295-2303

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.1142/S1793042115501043