The Riemann hypothesis and tachyonic off-shell string scattering amplitudes

Abstract The study of the $$\mathbf{4}$$ 4 -tachyon off-shell string scattering amplitude $$ A_4 (s, t, u) A ( s , t u ) , based on Witten’s open field theory, reveals existence poles in s -channel and associated to a continuum complex “spins” J . latter belong Regge trajectories t u channels which are defined by - (t) = 1 { 1\over 2 } \beta (t)= + i \lambda - J = 1 2 β + i λ ; (u) \gamma γ with real$$ r e a l These values ( ), given $${ \pm ± respectively, coincide precisely location critical line nontrivial Riemann zeta zeros \zeta (z_n _n) 0$$ ζ z n 0 It is argued that despite assigning angular momentum (spin) mass external tachyons along their not physically meaningful, net zero-spin value k_1 ) (k_2) k_3 k_4 k 3 meaningful because on-shell tachyon exchanged has well zero-spin. We proceed prove if there were (violating Hypothesis) outside Real~ z 1/2 R / (but inside strip) these putative don't$$ d o ′ correspond any finalize some concluding remarks sinh 0 \pi n$$ π continuous spins, non-commutative geometry other relevant topics.