In this paper we show that the maximum of a polynomial P ∈ ℂ[ z ] of degree d ≥ 2 in the unit disc can be bounded below by the sum of moduli of its two coefficients, say, for z s and z t under certain assumption on the pair s < t . We also show that this assumption on s , t cannot be removed or weakened and give several examples showing when this lower bound is (or is not) attained.

中文翻译：

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单位圆盘中多项式最大值的下界

在本文中，我们证明了单位圆盘中 d ≥ 2 次的多项式 P ∈ ℂ[ z ] 的最大值可以由其两个系数的模数之和来下界，例如，对于 zs 和 zt 在某些假设下对 s < t 。我们还表明，对 s , t 的这个假设不能被删除或削弱，并给出了几个例子来说明何时（或未）达到这个下界。