One computational approach in support of the Riemann hypothesis

Some of the results on the criteria for the existence of an analytic continuation into a domain of a function given on a part of its boundary obtained by one of the authors are applied to the Riemann Hypothesis on the zeta-function zeroes. We include all of the basic structural information needed on the previous results on analytic continuation. Some comprehensive numerical experiments have been performed. We have found two important trends in the associated numerical results. The first one is that these findings favor the view that the Riemann Hypothesis is valid. The second one corresponds to a new conjecture on monotonic behavior of some sequences of integrals. The computational experiments have been performed with the Mathematica V3.0.