论文标题
雅各比 - 佩隆算法的三个主题2
Three subjects of the Jacobi-Perron algorithm of dimension 2
论文作者
论文摘要
我们将研究维度2的Jacobi-Perron算法的三个主题。首先，我们研究“理想收敛”。关于近似值（p_n/r_n，q_n/r_n）to（a，b）（其中a和b是正实数，r_n，p_n和q_n是自然数），显示了| p_n-ar_n |的一些不平等和评估| | q_n-br_n |，我们将证明P_N-AR_N和Q_N-BR_N在0处收敛的一些足够条件，在这种情况下，算法被认为是理想的收敛性（请参见[1]）。其次，与经典的持续分数有关，我们处理代数共轭物的行为。第三，我们将证明（a，b）的集合从上方界定的（a，b）的集合是无效的，这是对[3]中定理196的概括。
We shall study three subjects of the Jacobi-Perron Algorithm of dimension 2. First, we study the "ideal convergence". About the approximations (p_n/r_n, q_n/r_n) to (A, B) (where A and B are positive real numbers, r_n, p_n and q_n are natural numbers), Showing some inequalities and evaluations of |p_n-Ar_n| and |q_n-Br_n|, we shall prove some sufficient conditions for p_n-Ar_n and q_n-Br_n converge at 0, in which case the algorithm is said to be ideally convergent(see [1]). Second, in connection with the classical continued fractions, we treat the behavior of the algebraic conjugates. Third, we shall prove that the set of (A, B) for which the digits of expansions are bounded from above is null which is a generalization of Theorem 196 in [3].
