This article establishes 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.

中文翻译：

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在Dedekind zeta函数的显式零自由区域上

本文为Dedekind zeta函数建立了新的显式零零区。我们证明的两个关键要素是非负，偶数，三角多项式和Dedekind zeta函数的所谓差分对数导数的显式公式的显式上限。我们对这种最后结果的改进来自两个方面。首先，我们的计算使用多项式，该多项式已通过模拟退火针对类似问题进行了优化。其次，我们为上述显式公式建立了更清晰的上限。