Multi-fold sums from a set with few products
classification
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keywords
cdotconstantsexistfinitefracgeq2multi-foldnumbers
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In this paper we show that for any $k\geq2$, there exist two universal constants $C_k,D_k>0$, such that for any finite subset $A$ of positive real numbers with $|AA|\leq M|A|$, $|kA|\geq \frac{C_k}{M^{D_k}}\cdot|A|^{\log_42k}.$
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