论文标题
在de bruijn-Newman Constant上：一种新方法
On the de Bruijn-Newman constant: a new approach
论文作者
论文摘要
纽曼（Newman）于1976年提出的纽曼（Newman）的猜想指出，$ξ_\ aleph \ left（λ\ right）$的所有零为$ \ aleph \ in \ mathbb {r} $都是真实的。它的等价语句是$ \ mathbb {m} _ \ aleph \ left（τ\ right）$具有纯粹的假想零，用于$ \ aleph \ in \ mathbb {r} $。众所周知，$ \ mathbb {m} _ \ aleph \ left（τ\ right）$是订单ONE的全部函数。本文通过Hadamard和Csordas，Norfolk和Varga的作品解决了$ \ Mathbb {M} _ \ Aleph \ left（τ\右）$的产品表示形式。我们通过其系列和产品建立了新的$ \ mathbb {m} _ \ aleph \ left（τ\ right）$。基于获得的结果，我们证明它仅具有纯粹的虚构零，以$ \ aleph \ in \ mathbb {r} $。这意味着纽曼的猜想是正确的。
The conjecture of Newman, proposed in 1976 by Newman, states that all zeros of $Ξ_\aleph \left( λ\right)$ are real for $\aleph \in \mathbb{R}$. Its equivalent statement is that $\mathbb{M}_\aleph \left( τ\right)$ has purely imaginary zeros for $\aleph \in \mathbb{R}$. It is well known that $\mathbb{M}_\aleph \left( τ\right)$ is an even entire function of order one. This article addresses the product representation for $\mathbb{M}_\aleph \left( τ\right)$ by the works of Hadamard and Csordas, Norfolk and Varga. We establish a new class of $\mathbb{M}_\aleph \left( τ\right)$ by its series and product. Based on the obtained result, we prove that it has only purely imaginary zeros for $\aleph \in \mathbb{R}$. This implies that the conjecture of Newman is true.
