论文标题
Quaternion $ p $ - 亚种持续分数
Quaternionic $p$-adic continued fractions
论文作者
论文摘要
我们开发了一个$ p $ - adiC的持续分数，用于$ \ mathbb q $ y mathbb q $以有效的prime $ p $分解。在这种情况下，也可以证明在交换案例中持有的许多属性。特别是，我们将注意力集中在具有有限分数扩展的元素的表征上。通过适当的Quaternionic高度概念，我们证明了有限性的标准。此外，我们对$ b $系数的二次多项式方程的解决方案造成了一些后果。
We develop a theory of $p$-adic continued fractions for a quaternion algebra $B$ over $\mathbb Q$ ramified at a rational prime $p$. Many properties holding in the commutative case can be proven also in this setting. In particular, we focus our attention on the characterization of elements having a finite continued fraction expansion. By means of a suitable notion of quaternionic height, we prove a criterion for finiteness. Furthermore, we draw some consequences about the solutions of a family of quadratic polynomial equations with coefficients in $B$.
