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# An Improved Sum–Product Inequality in Fields of Prime Order

International Mathematics Research Notices, no. 16 (2012): 3693-3705

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This note proves the sum–product inequality ${\mathrm max}(|A\cdot A|,\ |A+A|)\gg|A|^{1+\frac {1}{11}}\frac {1}{{\mathrm log}^{\frac {4}{11}}|A|},$ for sets of cardinality $1<|A|<\sqrt{p}$ in prime fields $\mathbb F_p$.

Michael Rudnev
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