Motivic zeta function

In algebraic geometry, the motivic zeta function of a smooth algebraic variety ${\displaystyle X}$ is the formal power series

Here ${\displaystyle X^{(n)}}$ is the ${\displaystyle n}$-th symmetric power of ${\displaystyle X}$, i.e., the quotient of ${\displaystyle X^{n}}$ by the action of the symmetric group ${\displaystyle S_{n}}$, and ${\displaystyle [X^{(n)}]}$ is the class of ${\displaystyle X^{(n)}}$ in the ring of motives (see below).

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