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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 zeroes of a polynomial are its roots by the fundamental theorem of algebra. The derivative of a continuous, differentiable function that twice crosses the axis must have a zero. The nontrivial zeros of the Riemann zeta function may all lie on the critical line. ( 1 mathematics, algebra) The additive identity element of a monoid or greater algebraic structure, particularly a group or ring.