Riemann Hypothesis/Zeroes

Zeroes of Riemann Zeta Function

Some of the zeroes of Riemann $\zeta$ function are positioned as follows:

Trivial Zeroes of Riemann Zeta Function are Even Negative Integers

Let $\rho = \sigma + i t$ be a zero of the Riemann zeta function not contained in the critical strip:

$0 \le \map \Re s \le 1$

Then:

$s \in \set {-2, -4, -6, \ldots}$

These are called the trivial zeros of $\zeta$.

First zero

The first zero of the Riemann $\zeta$ function is positioned at:

$\dfrac 1 2 + i \paren {14 \cdotp 13472 \, 5 \ldots}$