论文标题
来自2-D主成分分析和及时构图的分区$ \ MATHCAL {P} $ dirichlet eta函数模量的下限
A lower bound for the modulus of the Dirichlet eta function on a partition $\mathcal{P}$ from 2-D principal component analysis and transitive composition
论文作者
论文摘要
目前的手稿旨在得出DIRICHLET ETA函数模量垂直线$ \ re（s）=α$的模量下限的表达式。该方法采用构建基于参数椭圆的二维主成分分析的概念，以匹配复杂平面的维度。 \ Mathbb {C} $ s.t.的单侧下限$ \ forall s \ $ \ re（s）\ in \ mathcal {p} $，$ | η（s）| \ geq \ left | 1- \ frac {\ sqrt {2}} {2^α} \ right | $，其中$η$是dirichlet eta函数，与riemann假设相关，为$ | |η（s）| > 0 $ for \ in \ mathbb {c} $ s.t。 $ \ re（s）\ in \ Mathcal {p} $，其中$ \ Mathcal {p} $是跨越关键带的一半的分区，具体取决于变量。我们提出了复合下限$ \ forall s \ in \，\ mathbb {c} $ s.t.。 $ \ re（s）\ in \，] 1/2,1 [$，$ |η（s）| \ geq \ text {min} \ left（1- \ frac {\ sqrt {2}}} {2^α}，\ frac {\ sqrt {2}} {2^α} {2^α} - \ frac {\ sqrt {\ sqrt {\ sqrt {2}} = \ left（1- \ frac {2} {2^s} \ right）ζ$。作为创始原理，指的是$ \ Mathcal {l}^2 $ - 问题的解决方案的解决方案空间是由解释变量跨越其代数形式所跨越的空间的表示。
The present manuscript aims to derive an expression for the lower bound of the modulus of the Dirichlet eta function on vertical lines $\Re(s)=α$. The approach employs concepts of two-dimensional principal component analysis built on a parametric ellipse, to match the dimensionality of the complex plane. The one-sided lower bound $\forall s \in \mathbb{C}$ s.t. $\Re(s) \in \mathcal{P}$, $| η(s) | \geq \left| 1 - \frac{\sqrt{2}}{2^α} \right|$, where $η$ is the Dirichlet eta function, is related with the Riemann hypothesis as $|η(s)| > 0$ for any $s \in \mathbb{C}$ s.t. $\Re(s) \in \mathcal{P}$, where $\mathcal{P}$ is a partition spanning one half of the critical strip depending upon a variable. We propose the composite lower bound $\forall s \in \, \mathbb{C}$ s.t. $\Re(s) \in \,]1/2,1[$, $|η(s)| \geq \text{Min}\left(1- \frac{\sqrt{2}}{2^α},\frac{\sqrt{2}}{2^α}-\frac{\sqrt{2}}{2}\right)$, resulting from transitive composition in $η(s) = \left(1-\frac{2}{2^s} \right) ζ(s)$. As a founding principle, the solution space of the set of solutions referring to such $\mathcal{L}^2$-problem is a representation of the space spanned by explanatory variables satisfying its algebraic form.
