An Improved Sum-Product Bound for Quaternions

SIAM JOURNAL ON DISCRETE MATHEMATICS（2019）

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摘要

We show that there exists an absolute constant c > 0, such that, for any finite set A of quaternions, max{vertical bar A + A vertical bar; vertical bar AA vertical bar} greater than or similar to vertical bar A vertical bar(4/3+c): This generalizes a sum-product bound for real numbers proved by Konyagin and Shkredov.

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关键词

additive combinatorics,sum-product conjecture,quaternions

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