Refinement of an estimate for the Hurwitz zeta function in a neighbourhood of the line σ = 1
Volume 89 / 1999
Acta Arithmetica 89 (1999), 301-309
DOI: 10.4064/aa-89-4-301-309
Abstract
The well-known estimate of the order of the Hurwitz zeta function
$ζ(s,α) - α^{-s} ≪ t^{c(1-σ)^{3/2}} log^{2/3}t$
0.
The improvement of the constant c is a consequence of some technical modifications in the method of estimating exponential sums sketched by Heath-Brown ([11], p. 136).
