论文标题
连续，Chebyshev多项式和Riley多项式
Continuant, Chebyshev polynomials, and Riley polynomials
论文作者
论文摘要
在上一篇论文中，我们表明，每个2桥结$ k $的Riley多项式$ \ MATHCAL {R} _K（λ）$分为$ \ MATHCAL {r} _K（-u^2）= \ pm g（u^）= \ pm g（u）g（u）g（u）g（-u）g（-u）$ g（-u）$ g（u）$ g（u）$ g（u）在本文中，我们研究了Riley多项式的这种分裂特性。我们表明，Riley多项式可以用“ $ε$ -Chebyshev多项式”来表示，这是Chebyshev多项式的概括，其中包含$ε_i$ -semece $（ε_i=（ε_i=（ε_i=（ - 1）^{[I \fracβα] $ y $ s的信息）和2- $ k的$ k =分裂多项式$ g（u）$的明确公式，也是$ε$ -Chebyshev多项式。作为应用，我们发现了Riley多项式的不可约性的足够条件，并显示了对称Riley多项式的单峰特性。
In the previous paper, we showed that the Riley polynomial $\mathcal{R}_K(λ)$ of each 2-bridge knot $K$ is split into $\mathcal{R}_K(-u^2)=\pm g(u)g(-u)$, for some integral coefficient polynomial $g(u)\in \mathbb Z[u]$. In this paper, we study this splitting property of the Riley polynomial. We show that the Riley polynomial can be expressed by `$ε$-Chebyshev polynomials', which is a generalization of Chebyshev polynomials containing the information of $ε_i$-sequence $(ε_i=(-1)^{[i\fracβα]})$ of the 2-bridge knot $K=S(α,β)$, and then we give an explicit formula for the splitting polynomial $g(u)$ also as $ε$-Chebyshev polynomials. As applications, we find a sufficient condition for the irreducibility of the Riley polynomials and show the unimodal property of the symmetrized Riley polynomial.
