Padé approximation for a class of hypergeometric functions and parametric geometry of numbers
Padé approximation for a class of hypergeometric functions and parametric geometry of numbers
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一类超几何函数和数参数几何的 Padé 近似
DOI：
10.1016/j.jnt.2022.05.009
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发表时间：
2022
影响因子：
0.7
通讯作者：
Anthony Poels
中科院分区：
文献类型：
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作者：
M. Kawashima;Anthony Poels
本文给出了一类超几何函数（包括移位对数函数、二项式函数和移位指数函数）值的新的无理性测度。我们明确地构造Padé近似，通过使用一种形式化的方法，并表明相关的序列满足庞加莱型递归。为了精确地研究这类序列的渐近性态，我们建立了Poincaré-Perron定理的一个有效形式.因此，我们得到，除其他外，有效的非理性措施的值二项式函数在有理数，这可能有有用的算术应用。我们需要的一个一般性定理的同时合理的逼近证明，通过使用新的论点依赖于参数几何的号码。
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 aneffectiveversion 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.
代数点上的多对数可以线性无关吗？
影响因子：
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作者：
Sinnou David;Noriko Hirata-Kohno and Makoto Kawashima
通讯作者：
Noriko Hirata-Kohno and Makoto Kawashima