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A sum-product estimate in algebraic division algebras

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Abstract

LetA be a finite subset of some normed division algebra over ℝ with cardinality ⋎A⋎. We prove that either the sum set or the product set ofA has cardinality ⋎A⋎1+δ for some δ>0.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92521, Riverside, CA, USA

    Mei-Chu Chang

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  1. Mei-Chu Chang
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Additional information

Partially supported by NSA grant No. MDA 904-03-1-0045.

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Chang, MC. A sum-product estimate in algebraic division algebras. Isr. J. Math. 150, 369–380 (2005). https://doi.org/10.1007/BF02762388

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  • DOI: https://doi.org/10.1007/BF02762388

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