Understanding the Zeros of the Riemann Zeta Function 🔍

The Riemann Zeta Function can never become zero as it is a divergent series. We show a formula which approximately evaluates this divergent sum for any finite number of series terms. It is in fact the Dirichlet Eta Series which becomes zero. We can simply test that assertion numerically or computationally.

Dirichlet eta series is the same as Riemann zeta series but with a negative sign in front of alternating terms. When we consider the proper relationship between Zeta and Eta series using "finite" series terms, we can easily prove that the Eta series becomes zero when the real part of the exponent = 1/2. Perhaps by using the "infinite" series terms, we may never get this proof.