An application of kissing number in sum-product estimates
Sign Up to like & getrecommendations! Published in 2017 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-018-0831-x
Abstract: AbstractThe boundedness of the kissing numbers of convex bodies has been known to Hadwiger [9] for long. We present an application of it to the sum-product estimate $$\max(\mid{\mathcal{A}+\mathcal{A}}\mid,\mid{\mathcal{A}\mathcal{A}}\mid)\gg \frac {\mid{\mathcal{A}\mid}^{4/3}}{\lceil\log\mid{\mathcal{A}\mid} \rceil^{1/3}}$$max(∣A+A∣,∣AA∣)≫∣A∣4/3⌈log∣A∣⌉1/3for finite sets $${\mathcal{A}}$$A of… read more here.
Keywords: application kissing; sum product; mathcal mid; mid mathcal ... See more keywords