Hankel determinants, Pade approximations, and irrationality exponents for p-adic numbers
Hankel determinants, Pade approximations, and irrationality exponents for p-adic numbers
复制标题
p 进数的 Hankel 行列式、Pade 近似和无理指数
DOI：
10.1007/s10231-016-0602-7
复制
发表时间：
2017
影响因子：
1
通讯作者：
Yao Jia-Yan
中科院分区：
文献类型：
--
作者：
Bugeaud Yann;Yao Jia-Yan
无理p-adic数的无理指数是有理数对p-adic数的逼近速度的度量，一般很难显式计算。在这项工作中，我们将证明大类的自动p-adic数和Mahlerp-adic数（这是超越的）的无理性指数正好等于2。我们的类包含Thue-Morse-Mahlerp-adic数，正则paperfoldingp-adic数，Sternp-adic数等。
The irrationality exponent of an irrationalp-adic number, which measures the approximation rate ofby rational numbers, is in general very difficult to compute explicitly. In this work, we shall show that the irrationality exponents of large classes of automaticp-adic numbers and Mahlerp-adic numbers (which are transcendental) are exactly equal to 2. Our classes contain the Thue–Morse–Mahlerp-adic numbers, the regular paperfoldingp-adic numbers, the Sternp-adic numbers, among others.