论文标题
当前没有理由怀疑Riemann假设：Zeta功能超出了计算的范围
Currently there are no reasons to doubt the Riemann Hypothesis: The zeta function beyond the realm of computation
论文作者
论文摘要
我们研究了发表的论点，这些论点表明Riemann假设可能不是事实。在每种情况下，我们都提供证据来解释为什么声称的论点没有提供怀疑Riemann假设的充分理由。我们引用的证据涉及分析数理论中定理的混合物，随机矩阵理论中的定理以及涉及随机统一矩阵的特征多项式的说明性示例。也提供了四个错误的概念，这些概念在文献中反复出现有关zeta功能的计算。一个基于某些论点的基本问题是：Riemann Zeta功能的图表在其最大价值观的邻居中是什么样的？我们详细探讨了这个问题，并提供了有关L功能与随机矩阵的特征多项式之间关系的结果调查。我们强调了载波波的新兴现象起着的关键作用，这是由零密度的波动引起的。本文的要点是，可以在很大的高度上理解Zeta功能的某些方面，但是计算证据是误导的。
We examine published arguments which suggest that the Riemann Hypothesis may not be true. In each case we provide evidence to explain why the claimed argument does not provide a good reason to doubt the Riemann Hypothesis. The evidence we cite involves a mixture of theorems in analytic number theory, theorems in random matrix theory, and illustrative examples involving the characteristic polynomials of random unitary matrices. Similar evidence is provided for four mistaken notions which appear repeatedly in the literature concerning computations of the zeta-function. A fundamental question which underlies some of the arguments is: what does the graph of the Riemann zeta-function look like in a neighborhood of its largest values? We explore that question in detail and provide a survey of results on the relationship between L-functions and the characteristic polynomials of random matrices. We highlight the key role played by the emergent phenomenon of carrier waves, which arise from fluctuations in the density of zeros. The main point of this paper is that it is possible to understand some aspects of the zeta function at large heights, but the computation evidence is misleading.
