English

Breaking the 6/5 threshold for sums and products modulo a prime

Combinatorics 2018-06-20 v1 Number Theory

Abstract

Let AFpA \subset \mathbb{F}_p of size at most p3/5p^{3/5}. We show A+A+AAA6/5+c,|A+A| + |AA| \gtrsim |A|^{6/5 + c}, for c=4/305c = 4/305. Our main tools are the cartesian product point--line incidence theorem of Stevens and de Zeeuw and the theory of higher energies developed by the second author.

Keywords

Cite

@article{arxiv.1806.07091,
  title  = {Breaking the 6/5 threshold for sums and products modulo a prime},
  author = {G. Shakan and I. D. Shkredov},
  journal= {arXiv preprint arXiv:1806.07091},
  year   = {2018}
}
R2 v1 2026-06-23T02:34:19.455Z