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Riemann zeta function for nonnegative even integers. The Riemann zeta function for negative even integers is 0 (those are the trivial zeros of the Riemann zeta function). The Riemann zeta function for nonnegative even integers is given by (note that is the only rational number for nonnegative even integers) where are the Bernoulli numbers.
The following infinite series converges for all complex numbers with real part greater than 1, and defines in the complex plane to the right of the critical strip, i.e. for , where, in Euler's product (for the Riemann zeta function), the product is taken over all primes .