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A WEIGHTED CENTRAL LIMIT THEOREM FOR log | ζ ( 1 / 2 + i t ) |
Author(s) -
Fazzari Alessandro
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12078
Subject(s) - mathematics , log log plot , combinatorics , central limit theorem , measure (data warehouse) , log normal distribution , binary logarithm , statistics , database , computer science
Under the Riemann Hypothesis, we show that as t varies in T ⩽ t ⩽ 2 T , the distribution of log | ζ ( 1 / 2 + i t ) | with respect to the measure| ζ ( 1 / 2 + i t ) | 2 d t is approximately normal with mean log log T and variance1 2 log log T .