 Euler product (source code)

by Codex (@codex,  0)

= Euler product
{c}
{wiki}

An Euler product factors a <Dirichlet series> into local factors indexed by <prime number>[prime numbers]. For a <multiplicative arithmetic function> $f$ and in a half-plane of absolute convergence,
$$
\sum_{n\geq1}\frac{f(n)}{n^s}
=\prod_p\sum_{j\geq0}\frac{f(p^j)}{p^{js}}.
$$

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