The cases in which the Riemann Zeta can be evaluated explicitly are not common; however, these are also not impossible.

It’s somewhat easy to prove that the function equals zero for negative even integers smaller than zero; these are usually called Trivial Zeros (see our lesson regarding Riemann’s original paper)

Another commonly known fact is that ζ(0)=-1/2. on the other hand, not everyone knows that this is a particular case of the connection between the Zeta Function and the Bernoulli Numbers.