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

2018/06/19 by George Shakan, Shakan, G., Ilya D. Shkredov +1
Computer Science · Mathematics · #11P99 #11T99 #Analytic Number Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1806.07091

openalex publication_date 2018/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A ⊂ \mathbbF_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.

Citations

• On the number of sums and products

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