论文标题
收敛到代数数的一些算术特性
Some arithmetical properties of convergents to algebraic numbers
论文作者
论文摘要
令$ξ$为非理性代数实数，$（p_k / q_k）_ {k \ ge 1} $表示其收敛序列。令$（u_n）_ {n \ geq 1} $为整数的非分级线性复发序列，这不是多项式序列。我们表明，如果序列的相交$（q_k）_ {k \ ge 1} $和$（u_n）_ {n \ geq 1} $是无限的，那么$ξ$是二次数字。我们还讨论了序列$（q_k）_ {k \ ge 1} $的几个算术属性。
Let $ξ$ be an irrational algebraic real number and $(p_k / q_k)_{k \ge 1}$ denote the sequence of its convergents. Let $(u_n)_{n \geq 1}$ be a non-degenerate linear recurrence sequence of integers, which is not a polynomial sequence. We show that if the intersection of the sequences $(q_k)_{k \ge 1}$ and $(u_n)_{n \geq 1}$ is infinite, then $ξ$ is a quadratic number. We also discuss several arithmetical properties of the sequence $(q_k)_{k \ge 1}$.
