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Improved bounds for arithmetic progressions in product sets

Dmitrii Zhelezov (Institutionen för matematiska vetenskaper, matematik)
International Journal of Number Theory (1793-0421). Vol. 11 (2015), 8, p. 2295-2303.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Product sets; arithmetic progressions; polynomials; prime factors

Denna post skapades 2015-12-03. Senast ändrad 2016-11-07.
CPL Pubid: 227094


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