On a question of Cochrane and Pinner concerning multiplicative subgroups

2010/08/04 by Tomasz Schoen, T. Schoen, Schoen, T. +3
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1008.0723

8 pages; Quart. J. Math. (2011), 1-10

openalex publication_date 2010/08/04 · arxiv created 2011/05/27 · arxiv updated 2011/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Answering a question of T. Cochrane and C. Pinner, we prove that for any ε>0, sufficiently large prime number p and an arbitrary multiplicative subgroup R of the field Z/pZ, p^ε < |R| < p^2/3-ε the following holds |R + R|, |R - R| > |R|^3/2+δ, where δ>0 depends on ε only.

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