An application of kissing number in sum-product estimates
An application of kissing number in sum-product estimates
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接吻数在和积估计中的应用
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
C. Wong
中科院分区：
文献类型：
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作者：
J. Solymosi;C. Wong
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
$$max(mid{mathcal{A}+mathcal{A}}mid,mid{mathcal{A}mathcal{A}}mid)gg frac {mid{mathcal{A}mid}^{4/3}}{lceillogmid{mathcal{A}mid}
ceil^{1/3}}$$max(∣A+A∣,∣AA∣)≫∣A∣4/3⌈log∣A∣⌉1/3for finite sets $${mathcal{A}}$$A of quaternions and of a certain family of well-conditioned matrices.
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
$$max(mid{mathcal{A}+mathcal{A}}mid,mid{mathcal{A}mathcal{A}}mid)gg frac {mid{mathcal{A}mid}^{4/3}}{lceillogmid{mathcal{A}mid}
ceil^{1/3}}$$max(∣A+A∣,∣AA∣)≫∣A∣4/3⌈log∣A∣⌉1/3for finite sets $${mathcal{A}}$$A of quaternions and of a certain family of well-conditioned matrices.