A Further Step in the Proof of Riemann Hypothesis

A further step in the strategy for proving Riemann hypothesis proposed earlier(M. Pitkänen, math.GM/0102031) is suggested. The vanishing of Rieman Zeta reduces to an orthogonality condition for the eigenfunctions of a non-Hermitian operator D having the zeros of Riemann Zeta as its eigenvalues. The construction of D is inspired by the conviction that Riemann Zeta is associated with a physical system allowing superconformal transformations as its symmetries. The eigenfunctions of D are analogous to the so called coherent states and in general not orthogonal to each other. The states orthogonal to a vacuum state (having a negative norm squared) correspond to the zeros of Riemann Zeta. The physical states having a positive norm squared correspond to the zeros of Riemann Zeta at the critical line Re[s] = 1/2 and possibly those having Re[s] > 1/2. Riemann hypothesis follows by reductio ad absurdum from the hypothesis that the states corresponding to the zeros of Riemann Zeta with Re[s] < 1/2 allow a Fourier expansion in the basis provided by the states having Re[s] ≥ 1/2.