  This paper is a continuation of our recent paper with the same title,
arXiv:0806.1596v1 [math.NT], where a number of integral equalities involving
integrals of the logarithm of the Riemann zeta-function were introduced and it
was shown that some of them are equivalent to the Riemann hypothesis. A few new
equalities of this type are established; contrary to the preceding paper the
focus now is on integrals involving the argument of the Riemann zeta-function
(imaginary part of logarithm) rather than the logarithm of its module (real
part of logarithm). Preliminary results of the numerical research performed
using these equalities to test the Riemann hypothesis are presented. Our
integral equalities, together with the equalities given in the previous paper,
include all earlier known criteria of this kind, viz. Wang, Volchkov and
Balazard-Saias-Yor criteria, which are certain particular cases of the general
approach proposed.
