The Roots of the Riemann Zeta Function

The Riemann Hypothesis & The Roots of the Riemann Zeta Function

Q. The Dirichlet series parts do not converge in the critical strip. How is it possible that these series parts can be compared and subtracted to produce roots in the Riemann zeta function?: A. It is true that the Dirichlet series parts do not converge in the critical strip. It is also true that the series parts cannot be compared and subtracted algebraically in the critical strip. However, at the roots of the Riemann zeta function in the critical strip, the two Dirichlet series parts are geometrically equivalent and can be subtracted in a geometric sense, thereby producing roots.
Q. Is the Dirichlet series representation of the Riemann zeta function meaningful in a geometric sense throughout the entire critical strip?: A. No. The Dirichlet series representation of the Riemann zeta function is meaningful geometrically only at the roots in the critical strip.
Q. The Dirichlet series representation of the Riemann zeta function does not converge in the critical strip. Therefore, all your work must be wrong. Comment on this.: A. It is true that the Dirichlet series representation of the Riemann zeta function does not converge algebraically in the critical strip. However, the Dirichlet series representation, in fact, converges geometrically at the roots - and only at the roots - in the critical strip. This is what the book is all about!