On Additive Bases of Sets with Small Product Set
Artikel i vetenskaplig tidskrift, 2018

We prove that finite sets of real numbers satisfying vertical bar AA vertical bar <= vertical bar A vertical bar (1+epsilon) with sufficiently small epsilon > 0 cannot have small additive bases nor can they be written as a set of sums B + C with vertical bar B vertical bar, vertical bar C vertical bar >= 2. The result can be seen as a real analog of the conjecture of Sarkozy that multiplicative subgroups of finite fields of prime order are additively irreducible.

Författare

Ilya D. Shkredov

Russian Academy of Sciences

Dmitrii Zhelezov

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)

5 1585-1599

Ämneskategorier

Algebra och logik

Subatomär fysik

Signalbehandling

DOI

10.1093/imrn/rnw291

Mer information

Senast uppdaterat

2018-08-31