Jensen多项式不是证明黎曼假设的合理途径
Jensen polynomials are not a plausible route to proving the Riemann Hypothesis
摘要：
最近的工作对詹森多项式的黎曼xi函数及其衍生物发现了连接到厄米多项式。这些结果被认为是黎曼假设的证据，而且这些结果还被认为是zeta函数零点的随机矩阵统计的一个重要结果。我们把这项工作的背景下，以前的结果，并解释为什么厄米多项式的外观是有趣的和令人惊讶的，并可能代表一种新的类型的普遍规律，细化M。贝瑞的“余弦是一个普遍吸引子”原理。然而，我们发现没有理由建议连接到黎曼假设，也没有建议连接到约束随机矩阵统计的L-函数的零点。这些考虑表明，詹森多项式，以及一大类相关的多项式，是没有用的攻击黎曼假设。我们提出了一般的标准，以确定是否等价的黎曼假设可能是有用的。
英文摘要：
Recent work on the Jensen polynomials of the Riemann xi-function and its derivatives found a connection to the Hermite polynomials. Those results have been suggested to give evidence for the Riemann Hypothesis, and furthermore it has been suggested that those results shed light on the random matrix statistics for zeros of the zeta-function. We place that work in the context of prior results, and explain why the appearance of Hermite polynomials is interesting and surprising, and may represent a new type of universal law which refines M. Berry's "cosine is a universal attractor" principle. However, we find there is no justification for the suggested connection to the Riemann Hypothesis, nor for the suggested connection to the conjectured random matrix statistics for zeros of L-functions. These considerations suggest that Jensen polynomials, as well as a large class of related polynomials, are not useful for attacking the Riemann Hypothesis. We propose general criteria for determining whether an equivalence to the Riemann Hypothesis is likely to be useful.
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