# Why are the trivial zeros negative even integers?

1. Dec 30, 2009

### beyond

$$\varsigma(s) = \sum^{\infty}_{n=1}n^{-s}$$

If you substitute a trivial zero, lets say -2. Wouldn't it be

$$\varsigma(s) = \sum^{\infty}_{n=1} = 1^2 + 2^2 + 3^2 + 4^2 + . . .$$

How would this series be equals to zero?

Thanks

2. Dec 30, 2009

### antm88

3. Dec 31, 2009

### beyond

So that means that the Riemann Hypothesis is based on the functional equation instead?

4. Jan 1, 2010

5. Jan 1, 2010

### fourier jr

& the bernoulli numbers, and the function $\xi$