论文标题
Riemann-Siegel公式对Riemann的Zeta功能的高精度计算，II
High Precision Computation of Riemann's Zeta Function by the Riemann-Siegel Formula, II
论文作者
论文摘要
(This is only a first preliminary version, any suggestions about it will be welcome.) In this paper it is shown how to compute Riemann's zeta function $ζ(s)$ (and Riemann-Siegel $Z(t)$) at any point $s\in\mathbf C$ with a prescribed error $\varepsilon$ applying the, Riemann-Siegel formula as described in my paper "High Precision ...我”，数学。 80（2011）995--1009。 这包括研究要计算多少个术语以及获得所需结果的精度。考虑了所有可能的错误，即使是使用数字的浮点表示固有的错误。结果已用于实施计算。这些程序已包含在Python的公共图书馆“ MPMATH”中，用于计算特殊功能。因此，它们也包括在鼠尾草中。
(This is only a first preliminary version, any suggestions about it will be welcome.) In this paper it is shown how to compute Riemann's zeta function $ζ(s)$ (and Riemann-Siegel $Z(t)$) at any point $s\in\mathbf C$ with a prescribed error $\varepsilon$ applying the, Riemann-Siegel formula as described in my paper "High Precision ... I", Math of Comp. 80 (2011) 995--1009. This includes the study of how many terms to compute and to what precision to get the desired result. All possible errors are considered, even those inherent to the use of floating point representation of the numbers. The result has been used to implement the computation. The programs have been included in"mpmath", a public library in Python for the computation of special functions. Hence they are included also in Sage.
