On an effective order estimate of the Riemann zeta function in the critical strip (Q749597)

The well-known explicit estimation of the order of the Riemann zeta function \[ | \zeta (\sigma +it)| \ll t^{c(1-\sigma)^{3/2}} \ln^{2/3}t \] for 1/2\(\leq \sigma \leq 1\) and \(t\geq 2\) [see \textit{H. E. Richert}, Math. Ann. 169, 97-101 (1967; Zbl 0161.048)] is proved with the constant \(c=21\). The improvement of the constant c is a consequence of some technical modifications in application of the Vinogradov's inequality for exponential sums with the constant improved by \textit{E. I. Panteleeva} [Mat. Zametki 44, 494-505 (1988); Engl. translation in Math. Notes 44, 750-757 (1988; Zbl 0654.10041)].