There Should Exist Tetradic Nontrivial Zeros of the Riemann Zeta Function off the Critical Line

It is proved that κ1 > Son , where, κ1 denotes the sum of the reciprocals of all nontrivial zeros of the Riemann zeta function ζ(s) within the critical strip, while Son represents the same sum taken strictly over all such zeros on the critical line. This result implies the existence of nontrivial zeros off the critical line. A contradiction can be obtained by first establishing the relation between κ1 and the analytic upper bound for Son via termwise scaling (i.e., enlarging terms), and then comparing that relation with the relation between κ1 and the numerical evaluation of this upper bound using Odlyzko’s first two million nontrivial zeros on the critical line.