论文标题
在Poupard和Kreweras多项式的根上
On the roots of the Poupard and Kreweras polynomials
论文作者
论文摘要
POUPARD多项式是一个带有整数系数的变量中的多项式，与Bernoulli和切线数紧密相关。他们还具有组合解释。我们证明，每个Poupard多项式都在单位圆上具有其所有根。我们还获得了Kreweras引入的另一个多项式序列并与Genocchi数字相关的相同特性。这是通过一般性陈述获得的，该声明关于某些作用于腔粒多项式的线性算子。
The Poupard polynomials are polynomials in one variable with integer coefficients, with some close relationship to Bernoulli and tangent numbers. They also have a combinatorial interpretation. We prove that every Poupard polynomial has all its roots on the unit circle. We also obtain the same property for another sequence of polynomials introduced by Kreweras and related to Genocchi numbers. This is obtained through a general statement about some linear operators acting on palindromic polynomials.
