A central limit theorem for the Birkhoff sum of the Riemann zeta-function over a Boolean type transformation

Tanja I. Schindler

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A central limit theorem for the Birkhoff sum of the Riemann zeta-function over a Boolean type transformation

机译：riemann zeta-function ov在布尔型转换中的中央极限定理

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摘要

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.

机译：我们证明了实部和虚部的中央极限定理以及沿着临界条中的垂直线采样的Riemann Zeta函数的绝对值，相对于类似于布尔转换的ergodic变换。这结果通过赋予谁证明了同一系统的强大规定的措施来补充结果。作为一个侧面结果，我们在相同的ergodic转换上规范了一类无界可观察到的一般中央极限定理。证据基于布尔型变换与加倍映射和转移操作方法之间的同构。

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来源
《Dynamical Systems》 |2020年第4期|682-703|共22页
作者
Tanja I. Schindler;
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作者单位

Centra di Ricerca Ennio De Giorgi Scuola Normale Superiore Pisa PI Italy;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
原文格式 PDF
正文语种 eng
中图分类
关键词
central limit theorem; Riemann zeta-function; transfer operator; Boolean transformation;

机译：中心极限定理;riemann zeta函数;转移运营商;布尔转型;

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1. A central limit theorem for coefficients of the modified Borwein method for the calculation of the Riemann zeta-function [J] . Belovas Igoris Lithuanian mathematical journal . 2019,第1期

机译：用于计算Riemann Zeta函数的改进Borwein方法系数的中央极限定理
2. Corrigendum to the paper "Limit theorems for the Mellin transform of the square of the Riemann zeta-function [J] . ANTANAS LAURINCIKAS Acta Arithmetica . 2010,第2期

机译：论文“ Riemann zeta函数平方的Mellin变换的极限定理”
3. Limit theorems for the Mellin transform of the fourth power of the Riemann zeta-function [J] . Laurincikas A Siberian Mathematical Journal . 2010,第1期

机译：黎曼zeta函数四次幂的Mellin变换的极限定理
4. Beyond the Central Limit theorem: Asymptotic Expansions and Pseudorandomness for Combinatorial Sums [C] . De Anindya IEEE Annual Symposium on Foundations of Computer Science . 2015

机译：超越中心极限定理：组合和的渐近展开性和伪随机性
5. Discrete local central limit theorems and boolean function complexity measures [D] . Gilmer, Justin. 2015

机译：离散局部中心极限定理和布尔函数复杂度测度
6. ω-Theorems for Riemanns Zeta-Function at Harmonic Combinations of Points [O] . Norman Levinson 1972

机译：点的调和组合时黎曼Zeta函数的ω-定理
7. A central limit theorem for the Birkhoff sum of the Riemann zeta-function over a Boolean type transformation [O] . Tanja I. Schindler 2020

机译：riemann zeta-function ov在布尔型转换中的中央极限定理
8. The Equivalence of Functional Central Limit Theorems for Counting Processes and Associated Partial Sums [R] . Iglehart, D. L., Whitt, W. 1969

机译：计数过程和相关部分和的功能中心极限定理的等价性

A central limit theorem for the Birkhoff sum of the Riemann zeta-function over a Boolean type transformation

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