Abstract
Abstract
We provide explicit bounds for the Riemann zeta-function on the line
$\mathrm {Re}\,{s}=1$
, assuming that the Riemann hypothesis holds up to height T. In particular, we improve some bounds in finite regions for the logarithmic derivative and the reciprocal of the Riemann zeta-function.
Publisher
Cambridge University Press (CUP)
Reference15 articles.
1. Mathematical Notes (5): On the Function 1/ζ(1+ti
)
2. [5] Johnston, D. R. , Ramaré, O. and Trudgian, T. , ‘An explicit upper bound for $L\left(1,\chi \right)$ when $\chi$ is quadratic’, Res. Number Theory 9 (2023), Article No. 72.
3. Accurate estimation of sums over zeros of the Riemann zeta-function
4. [10] Palojärvi, N. and Simonič, A. , ‘Conditional estimates for $L$ -functions in the Selberg class’, Preprint, 2023, arXiv:2211.01121.
5. Approximate formulas for some functions of prime numbers