  Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to
a certain weighted integral of the logarithm of the Riemann zeta-function along
the critical line equaling zero. Assuming the Riemann Hypothesis, we
investigate the rate at which a truncated version of this integral tends to
zero, answering a question of Borwein, Bradley, and Crandall and disproving a
conjecture of the same authors. A simple modification of our techniques gives a
new proof of a classical Omega theorem for the function S(t) in the theory of
the Riemann zeta-function.
