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Breaking the 6/5 threshold for sums and products modulo a prime
Published 19 Jun 2018 in math.CO and math.NT | (1806.07091v1)
Abstract: Let $A \subset \mathbb{F}_p$ of size at most $p{3/5}$. We show $$|A+A| + |AA| \gtrsim |A|{6/5 + c},$$ for $c = 4/305$. 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.
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