论文标题
在Dedekind Zeta功能的明确无零区域上
On an explicit zero-free region for the Dedekind zeta-function
论文作者
论文摘要
我们为Dedekind Zeta功能建立新的明确无零区域。我们证明的两个关键要素是无负的，即使是三角多项式和明确的上限，用于所谓的差异Zeta功能的所谓差异对数衍生物的显式公式。我们在此类结果中建立的改进来自两个来源。首先，我们的计算使用多项式，该多项式已通过模拟退火来优化类似问题。其次，我们为上述显式公式建立了更清晰的上限。
We establish new explicit zero-free regions for the Dedekind zeta-function. Two key elements of our proof are a non-negative, even, trigonometric polynomial and explicit upper bounds for the explicit formula of the so-called differenced logarithmic derivative of the Dedekind zeta-function. The improvements we establish over the last result of this kind come from two sources. First, our computations use a polynomial which has been optimised by simulated annealing for a similar problem. Second, we establish sharper upper bounds for the aforementioned explicit formula.
