A Slight Improvement to Garaev's Sum Product Estimate

2007/03/20 by Nets Hawk Katz, Katz, Nets Hawk, Chun‐Yen Shen +1 · 1 citation
Agricultural and Biological Sciences · #11T99 05D99 #Agricultural Economics and Practices #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0703614

openalex publication_date 2007/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We slightly improve Garaev's recent sum-product estimate largely by using Plunneke's inequality a little more efficiently. We improve the exponent from 15/14 to 14/13.

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• Additive congruences with factorials modulo a prime

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