One computational approach in support of the Riemann hypothesis

Some of the results on the criteria for the existence of an analytic contin uation 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-fu nction zeroes. We include all of the basic structural information needed on the previous results on analytic continuation. Some comprehensive numerica l experiments have been performed. We have found two important trends in th e associated numerical results. The first one is that these findings favor the view that the Riemann Hypothesis is valid. The second one corresponds t o a new conjecture on monotonic behavior of some sequences of integrals. Th e computational experiments have been performed with the Mathematica V3.0. (C) 1998 Elsevier Science Ltd. All rights reserved.