Explicit estimates for the Riemann zeta function
The authors apply van der Corput's method for the estimation of exponential sums to obtain useful explicit estimates for \(|\zeta(1/2+it)|\). Although not the strongest ones known, the bounds attained by the authors have the merit that they hold for all values of \(t\). For example, as a Corollary of their Theorem 3, it follows that \(|\zeta(1/2+it)| \leq 2.657\) if \(0 \leq t\leq \text{e}\), while for \(t\geq \text{e}\) one has \(|\zeta(1/2+it)| \leq 3t^{1/6}\log t\). The proofs rely on seven lemmas, in whose formulation and proofs care has been taken in order that all estimates are explicit. Applications of the results to prime numbers in short intervals are announced to be forthcoming.
scientific article; zbMATH DE number 2143226