  In this paper we study the function G(z) :=
  int{0,infinity} y^{z-1}(1 + \exp(y))^{-1} dy,
  for z in C. We derive a functional equation
  that relates G(z) and G(1 - z) for all z in C,
  and we prove:
  -- That G and the Riemann Zeta function Zeta have
  exactly the same zeros in the critical region
  D := z in C: Re z in (0,1);
  -- All the zeros of the Riemann Zeta function
  located on the critical line are simple; and
  -- The Riemann hypothesis, i.e., that all of the zeros
  of G in D are located on the critical line L :=
  {z in D : Re z = 1/2}.
