论文标题
帕德（Padé）的近似，用于数字函数和数字的参数几何形状
Padé approximation for a class of hypergeometric functions and parametric geometry of numbers
论文作者
论文摘要
在本文中，我们获得了属于特定类别的超几个体数函数的功能值的新非理性度量，包括移动的对数函数，二项式函数和转移的指数函数。我们通过使用形式方法明确构建帕德近似，并表明关联的序列满足了庞加莱型复发。为了精确研究这些序列的渐近行为，我们建立了poincaré-perron定理的\ emph {有效}版本。结果，除其他外，我们还获得了有效的非理性性度量，以合理数字的二项式函数值，这可能具有有用的算术应用。通过使用依靠数字参数几何形状的新参数来证明我们需要的同时理性近似的一般定理。
In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We explicitly construct Padé approximations by using a formal method and show that the associated sequences satisfy a Poincaré-type recurrence. To study precisely the asymptotic behavior of those sequences, we establish an \emph{effective} version of the Poincaré-Perron theorem. As a consequence we obtain, among others, effective irrationality measures for values of binomial functions at rational numbers, which might have useful arithmetic applications. A general theorem on simultaneous rational approximations that we need is proven by using new arguments relying on parametric geometry of numbers.
