On sets with small additive doubling in product sets

2015/02/12 by Dmitry Zhelezov, Zhelezov, Dmitry
Computer Science · Mathematics · #Advanced Graph Theory Research #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1502.03700

openalex publication_date 2015/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following the sum-product paradigm, we prove that for a set B with polynomial growth, the product set B.B cannot contain large subsets with size of order |B|² with small doubling. It follows that the additive energy of B.B is asymptotically o(|B|⁶). In particular, we extend to sets of small doubling and polynomial growth the classical Multiplication Table theorem of Erdős saying that |[1..n]. [1..n]| = o(n²).

Citations

• Linear Equations in Variables which Lie in a Multiplicative Group

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