On a question of Cochrane and Pinner concerning multiplicative subgroups

Details On a question of Cochrane and Pinner concerning multiplicative subgroups On a question of Cochrane and Pinner concerning multiplicative subgroups

2010-08-04

arxiv.org/abs/1008.0723v2

Mathematics

Number Theory

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

Scientific paper

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

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