Rational approximations to the dilogarithm
Rational approximations to the dilogarithm
复制标题
二对数的有理近似
DOI：
10.1090/s0002-9947-1993-1147401-5
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发表时间：
1993
影响因子：
1.3
通讯作者：
M. Hata
中科院分区：
文献类型：
--
作者：
M. Hata
给出了对数函数L 2(Z)在有理点z=1/k对任意整数k∈(−∞，−5]∪[7，∞)取值的无理性证明.为了证明这一点，我们发展了利用Legendre型多项式的Pade型逼近方法，该方法也得到了L 2(1/k)的良好的无理性度量。此外，对于每个整数k−5]∈(−∞，−[7，∪]，也得到了数1，−(1∈(−∞，−1/k)和L 2(1/k)在Q上的线性无关性。
The irrationality proof of the values of the dilogarithmic function L 2 (z) at rational points z = 1/k for every integer k ∈ (−∞, −5] ∪ [7, ∞) is given. To show this we develop the method of Pade-type approximations using Legendre-type polynomials, which also derives good irrationality measures of L 2 (1/k). Moreover, the linear independence over Q of the numbers 1, log(1 − 1/k), and L 2 (1/k) is also obtained for each integer k ∈ (−∞, −5] ∪ [7, ∞)