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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}.

All Zeros of the Riemann Zeta Function in the Critical Strip are Located on the Critical Line and are Simple