1. zeta zeros

Could someone please explain why the zeta function has trivial zeros at the negative even integers?

2. Originally Posted by bigdoggy
Could someone please explain why the zeta function has trivial zeros at the negative even integers?

The zeta function's Horowitz functional equation is

You can also use the above functional relation in its equivalent form $\displaystyle \zeta(1-s)=2(2\pi)^{-s}\,\Gamma(s)\cos\!\left(\frac{\pi s}{2}\right)\zeta(s)$

Tonio