Product sets cannot contain long arithmetic progressions

• Autorzy: Dmitrii Zhelezov
• Języki publikacji: EN

Abstrakty

EN

Let B be a set of complex 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((nlog²n)/(loglogn)) and present an example of a product set containing an arithmetic progression of length Ω(nlogn). For sets of complex numbers we obtain the upper bound $O(n^{3/2})$.

Kategorie tematyczne

• 11B25: Arithmetic progressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 163
• Numer: 4
• Strony: 299-307

Daty

wydano

2014

Twórcy

autor

Dmitrii Zhelezov

• Department of Mathematical Sciences, Chalmers University of Technology
• University of Gothenburg, 41296 Gothenburg, Sweden

Identyfikatory

DOI

10.4064/aa163-4-1