Slightly improved sum-product estimates in fields of prime order

2009/07/12 by Liangpan Li, Li, Liangpan
Computer Science · Mathematics · #11B75 #Analytic Number Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0907.2051

openalex publication_date 2009/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbbF_p be the field of residue classes modulo a prime number p and let A be a nonempty subset of \mathbbF_p. In this paper we show that if |A|\preceq p^0.5, then max\|A± A|,|AA|\\succeq|A|^13/12; if |A|\succeq p^0.5, then max\|A± A|,|AA|\\succapprox min\|A|^13/12(\frac|A|p^0.5)^1/12,|A|((p)/(|A|))^1/11\. These results slightly improve the estimates of Bourgain-Garaev and Shen. Sum-product estimates on different sets are also considered.

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