On Additive Bases of Sets with Small Product Set
Journal article, 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.

Author

Ilya D. Shkredov

Russian Academy of Sciences

Dmitrii Zhelezov

Chalmers, Mathematical Sciences, Analysis and Probability Theory

International Mathematics Research Notices

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

5 1585-1599

Subject Categories

Algebra and Logic

Subatomic Physics

Signal Processing

DOI

10.1093/imrn/rnw291

More information

Latest update

4/3/2019 2