2025/02/28 by Shkredov, Ilya D.
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2502.20702
We continue to study the relationship between the size of the sum of a set and the common energy of its subsets. We find a rather sharp subexponential dependence between the doubling constant of a set A and the minimal common energy taken over all partitions of A into two disjoint subsets. As an application, we give a proof of the well--known arithmetic regularity lemma with better dependence on parameters.