Explicit Bound of $\pmb{|\zeta\left(1+it\right)|}$
| Autor: | Qingyi, Eunice Hoo, Teo, Lee-Peng |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this work, we show that for all $t\geq e$, \[|\zeta(1+it)|\leq 0.6443 \log t. \] The equality is achieved when $t=17.7477$. We also use the Riemann-Siegel formula and numerical computations to show that \[|\zeta(1+it)|\leq\frac{1}{2}\log t+0.6633\hspace{1cm}\text{when}\;t\geq e.\]When $t\geq 100$, the bound $\frac{1}{2}\log t+0.6633$ is better than the bound $0.6443\log t$. Comment: 31 pages, 6 figures |
| Databáze: | arXiv |
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