• Corpus ID: 245329530

Additive energies on discrete cubes

  title={Additive energies on discrete cubes},
  author={Jaume de Dios Pont and Rachel Greenfeld and Paata Ivanisvili and Jos'e Madrid},
We prove that for d ≥ 0 and k ≥ 2, for any subset A of a discrete cube {0, 1}, the k−higher energy of A (the number of 2k−tuples (a1, a2, . . . , a2k) in A with a1−a2 = a3−a4 = · · · = a2k−1−a2k) is at most |A|2 k+2), and log2(2 +2) is the best possible exponent. We also show that if d ≥ 0 and 2 ≤ k ≤ 10, for any subset A of a discrete cube {0, 1}, the k−additive energy of A (the number of 2k−tuples (a1, a2, . . . , a2k) in A with a1 +a2 + · · ·+ak = ak+1 +ak+2 + · · ·+a2k) is at most |A|2 ( 2k… 

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