We use subsequence and moving average ergodic theorems applied to Boole's transformation and its variants and their invariant measures on the real line to give new characterisations of the Lindelöf Hypothesis and the Riemann Hypothesis. These ideas are then used to study the value distribution of Dirichlet L-functions, and the zeta functions of Dedekind, Hurwitz and Riemann and their derivatives. This builds on earlier work of R. L. Adler and B. Weiss, M. Lifshits and M. Weber, J. Steuding, J. Lee and A. I. Suriajaya using Birkhoff's ergodic theorem and probability theory.

中文翻译：

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关于良好的普遍性和黎曼假设

我们在实线上使用应用于Boole变换及其变体及其不变度量的子序列和移动平均遍历定理，以给出Lindelöf假说和Riemann假说的新特征。然后将这些思想用于研究Dirichlet L函数的值分布以及Dedekind，Hurwitz和Riemann及其衍生物的zeta函数。这是基于RL Adler和B. Weiss，M。Lifshits和M. Weber，J。Steuding，J。Lee和AI Suriajaya使用伯克霍夫的遍历定理和概率论进行的早期工作。