  An odd meromorphic function f(s) is constructed from the Riemann
zeta-function evaluated at one-half plus s. We determine the two-sided Laplace
transform representation of f(s) on open vertical strips, V'(4w), disjoint from
the (translated) critical strip. V'(4w) consists of all s with real part,
Re(s), of absolute value greater than one-half and Re(s) between successive
poles 4w, 4(w + 1) of f(s), with w an integer. The corresponding Laplace
density is related to confluent hypergeometric functions. That density is shown
to be positive for nonzero w other than -1. Those results are obtained without
relying on any unproven hypothesis. They are used together with the Riemann
hypothesis and hypotheses advanced by the author to obtain conditional results
concerning the zeta-function. Those results are presented in Part I. Their
proofs are derived in Parts III-V. A metric geometry expression of the
positivity of the Laplace densities arising is established in Part VI.
