Zolotarev的第五和第六个问题
Zolotarev's fifth and sixth problems
摘要：
在一个有影响力的1877年文件，Zolotarev问和回答四个问题的多项式和有理逼近。我们问和回答两个问题：什么是最好的合理逼近$r$和$s$ $\sqrt{z}$和$\mbox{sign}(z)$上的单位圆（不包括某些弧附近的不连续性），与属性，$|r(z)|=|s(z)|=1$为$|z|=1$？我们表明，这些问题的解决方案与Zolotarev的第三和第四个问题，在一个非平凡的方式。
英文摘要：
In an influential 1877 paper, Zolotarev asked and answered four questions about polynomial and rational approximation. We ask and answer two questions: what are the best rational approximants $r$ and $s$ to $\sqrt{z}$ and $\mbox{sign}(z)$ on the unit circle (excluding certain arcs near the discontinuities), with the property that $|r(z)|=|s(z)|=1$ for $|z|=1$? We show that the solutions to these problems are related to Zolotarev's third and fourth problems in a nontrivial manner.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
