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arXiv math/01021452001-02-19math.CAmath.FA

三元集的Sidon常数

The Sidon constant of sets with three elements

Stefan Neuwirth

备注：: 7 pages

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摘要：

本文解决了三角多项式的一个初等极值问题，得到了三元集{n 0，n1，n2}的Sidon常数的精确值：当n = max（n1-n 0，n2-n 0，n2-n1）/ gcd（n1-n 0，n2-n 0）时，Sidon常数为\sec（π/ 2n）.

英文摘要：

We solve an elementary extremal problem on trigonometric polynomials and obtain the exact value of the Sidon constant for sets with three elements {n0, n1, n2}: it is \sec(π/ 2n) for n = max(n1-n0, n2-n0, n2-n1) / gcd(n1-n0, n2-n0).

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