Advanced Search

The well-known estimate of the order of the Hurwitz zeta function      $\zeta (s,\alpha )-{\alpha }^{-s}\ll t^{c{(1-\sigma )}^{3/2}}lo{g}^{2/3}t$ 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).