An explicit upper bound for the Riemann zeta-function near the line \(\omega=1\)
The author proves the bounds \[ | \zeta(\sigma + it)| \leq 175t^{146(1-\sigma)^{3/2}}\log^{2/3}t \quad({\textstyle{1\over 2}} \leq \sigma \leq 1, t \geq 2) \] and \[ | \zeta(\sigma + it)| \leq 175\log^{2/3}t \qquad(\sigma \geq 1, t \geq 2). \] The merit of these results is that the numerical constants are all explicit, for otherwise the bounds are well-known. The proofs are based on careful, laborious estimations involving the known proofs. Each step of the proof is explicitly worked out.
scientific article; zbMATH DE number 1309612
scientific article