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

K Ramachandra (1)

1 TIFR - Tata Institute for Fundamental Research

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 $\varepsilon$.

Mots clés: L-function; zero-free regions; alternate intervals

Domaines: Mathématiques [math]

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