It is proved that Solymosi’s sum-product estimate max{|A + A|, |A · A|} ≫ |A|4/3/(log |A|)1/3 holds for any finite set A in an ordered field F.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 9, pp. 1257–1261, September, 2014.
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Xue, B. A Note on Solymosi’s Sum-Product Estimate for Ordered Fields. Ukr Math J 66, 1408–1413 (2015). https://doi.org/10.1007/s11253-015-1019-y
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DOI: https://doi.org/10.1007/s11253-015-1019-y