ABSTRACT We prove a central limit theorem for the real and imaginary part and the absolute value of the Riemann zeta-function sampled along a vertical line in the critical strip with respect to an ergodic transformation similar to the Boolean transformation. This result complements a result by Steuding who has proven a strong law of large numbers for the same system. As a side result we state a general central limit theorem for a class of unbounded observables on the real line over the same ergodic transformation. The proof is based on an isomorphism between the Boolean type transformation and the doubling map and on the transfer operator method.

中文翻译：

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布尔型变换上黎曼 zeta 函数的 Birkhoff 和的中心极限定理

摘要 我们证明了实部和虚部的中心极限定理以及沿临界带中垂直线采样的黎曼 zeta 函数的绝对值，该值相对于类似于布尔变换的遍历变换。这个结果补充了 Steuding 的结果，他证明了同一系统的强大数定律。作为附带结果，我们陈述了同一遍历变换上实线上的一类无界可观测量的一般中心极限定理。该证明基于布尔类型转换和加倍映射之间的同构以及转移算子方法。