Two identities extracted from the literature are coupled to obtain an integral equation for Riemann's ξ(s) function, and thus ζ(s) indirectly. The equation has a number of simple properties from which useful derivations flow, the most notable of which relates ζ(s) anywhere in the critical strip to its values on a line anywhere else in the complex plane. From this, I obtain both an analytic expression for ζ(σ + it) everywhere inside the asymptotic (t → ∞) critical strip, and an approximate solution, within the confines of which the Riemann Hypothesis is shown to be true. The approximate solution predicts a simple, but strong correlation between the real and imaginary components of ζ(σ + it ) for different values of σ and equal values of t ; this is illustrated in a number of figures.