- #1
Facktor
- 4
- 0
According to Wikipedia, the Zeta Riemann Function is defined as follows:
\begin{equation}
\zeta(z) = \sum_{k=1}^{\infty}\frac{1}{k^{z}}, \forall z \in \mathbb{C}, Re[Z] > 1.
\end{equation}
Well, the trivial zeros are the negative even numbers. Is that a consequence of the following expression?
\begin{equation}
\zeta(-n) = -\frac{B_{n+1}}{n+1}, n \geq 1, n \in \mathbb{I},
\end{equation}
where B is a Bernoulli number.
But the above expression is a definition of the Zeta Function for negative integers? Why?
Thanks!
\begin{equation}
\zeta(z) = \sum_{k=1}^{\infty}\frac{1}{k^{z}}, \forall z \in \mathbb{C}, Re[Z] > 1.
\end{equation}
Well, the trivial zeros are the negative even numbers. Is that a consequence of the following expression?
\begin{equation}
\zeta(-n) = -\frac{B_{n+1}}{n+1}, n \geq 1, n \in \mathbb{I},
\end{equation}
where B is a Bernoulli number.
But the above expression is a definition of the Zeta Function for negative integers? Why?
Thanks!