论文标题
代数函数的周期性点与Ramanujan的持续部分有关
Periodic points of algebraic functions related to a continued fraction of Ramanujan
论文作者
论文摘要
Ramanujan的持续分数$ v（τ）$在字段中的某些论点进行了评估，$ k = \ mathbb {q}（\ sqrt {-d}）$，带有$ -D \ equiv 1 $（mod $ 8 $），其中理想$（2）= \ wp_2 \ wp_2 \ wp_2 \ wp_2'$是两种primpless a产品。这些值的$ v（τ）$的值显示出生成$ \ wp_2 $或$ \ wp_2'$的惯性字段，这是在$ k $上的扩展环类字段中的。证明了这些相同值的$ \ mathbb {q} $，以及$ 0，-1 \ pm \ sqrt {2} $，被证明形成了固定代数函数$ \ hat f（x）$的确切定期点的确切点集。这些是Rogers-Ramanujan的相似结果的类似物。
A continued fraction $v(τ)$ of Ramanujan is evaluated at certain arguments in the field $K = \mathbb{Q}(\sqrt{-d})$, with $-d \equiv 1$ (mod $8$), in which the ideal $(2) = \wp_2 \wp_2'$ is a product of two prime ideals. These values of $v(τ)$ are shown to generate the inertia field of $\wp_2$ or $\wp_2'$ in an extended ring class field over the field $K$. The conjugates over $\mathbb{Q}$ of these same values, together with $0, -1 \pm \sqrt{2}$, are shown to form the exact set of periodic points of a fixed algebraic function $\hat F(x)$, independent of $d$. These are analogues of similar results for the Rogers-Ramanujan continued fraction.
