Weighted value distributions of the Riemann zeta function on the critical line
Weighted value distributions of the Riemann zeta function on the critical line
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黎曼 zeta 函数在临界线上的加权值分布
DOI：
10.1515/forum-2020-0284
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发表时间：
2021
影响因子：
0.8
通讯作者：
Alessandro Fazzari
中科院分区：
文献类型：
--
作者：
Alessandro Fazzari
Abstract We prove a central limit theorem for log|ζ(12+it)|{\log\lvert\zeta(\frac{1}{2}+it)\rvert} with respect to the measure |ζ(m)(12+it)|2kdt{\lvert\zeta^{(m)}(\frac{1}{2}+it)\rvert^{2k}\,dt} (k,m∈ℕ{k,m\in\mathbb{N}}), assuming RH and the asymptotic formula for twisted and shifted integral moments of zeta. Under the same hypotheses, we also study a shifted case, looking at the measure |ζ(12+it+iα)|2kdt{\lvert\zeta(\frac{1}{2}+it+i\alpha)\rvert^{2k}\,dt}, with α∈(-1,1){\alpha\in(-1,1)}. Finally, we prove unconditionally the analogue result in the random matrix theory context.
Abstract We prove a central limit theorem for log|ζ(12+it)|{\log\lvert\zeta(\frac{1}{2}+it)\rvert} with respect to the measure |ζ(m)(12+it)|2kdt{\lvert\zeta^{(m)}(\frac{1}{2}+it)\rvert^{2k}\,dt} (k,m∈ℕ{k,m\in\mathbb{N}}), assuming RH and the asymptotic formula for twisted and shifted integral moments of zeta. Under the same hypotheses, we also study a shifted case, looking at the measure |ζ(12+it+iα)|2kdt{\lvert\zeta(\frac{1}{2}+it+i\alpha)\rvert^{2k}\,dt}, with α∈(-1,1){\alpha\in(-1,1)}. Finally, we prove unconditionally the analogue result in the random matrix theory context.
影响因子：
3
作者：
Arguin, Louis-Pierre;Belius, David;Soundararajan, Kannan
通讯作者：
Soundararajan, Kannan
二次除数问题和黎曼 zeta 函数的矩
影响因子：
2.6
作者：
Bettin, Sandro;Bui, Hung;Li, Xiannan;Radziwiłł, Maksym
通讯作者：
Radziwiłł, Maksym