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# A remark on $\zeta(1+it).$

Abstract : Let $T\geq1000$ and $X = \exp(\log\log T/\log\log\log T)$. Consider any set $O$ of disjoint open intervals $I$ of length $1/X$, contained in the interval $T\leq t\leq T+e^X$. We prove in this paper, that $\vert\log\zeta(1+it)\vert\leq\varepsilon\log\log T$ in $O$ with the exception of $K$ intervals $I$, where $0<\varepsilon\leq1$ and $K$ depends only on $\varepsilon$.
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Journal articles
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Cited literature [2 references]

https://hal.archives-ouvertes.fr/hal-01104287
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Submitted on : Friday, January 16, 2015 - 2:42:09 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Friday, September 11, 2015 - 6:58:04 AM

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### Citation

K Ramachandra. A remark on $\zeta(1+it).$. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1987, Volume 10 - 1987, pp.2-8. ⟨10.46298/hrj.1987.101⟩. ⟨hal-01104287⟩

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