Euler product

In number theory, an Euler product is an expansion of a Dirichlet series into an infinite product indexed by prime numbers. The name arose from the case of the Riemann zeta-function, where such a product representation was proved by Leonhard Euler.

In general, if ${\displaystyle a}$ is a multiplicative function, then the Dirichlet series

is equal to

where the product is taken over prime numbers ${\displaystyle p}$, and ${\displaystyle P(p,s)}$ is the sum

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