  The purpose of the present paper is to reveal the relation between the
behavior of the logarithm of the Riemann zeta-function $\log{\zeta(s)}$ and the
distribution of zeros of the Riemann zeta-function. We already know some
examples for the relation by some previous works. For example, Littlewood
showed an upper bound of $\log{\zeta(1/2 + it)}$ by assuming the Riemann
Hypothesis in 1924. One of our results reveals that Littlewood's upper bound
can be proved without assuming a hypothesis as strong as the Riemann
Hypothesis.
