The Euler product formula is a representation of a function, particularly in number theory, which expresses a function as an infinite product over prime numbers. It is most famously used in relation to the Riemann zeta function, \( \zeta(s) \), for complex numbers \( s \) where the real part is greater than 1.
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An Euler product factors a Dirichlet series into local factors indexed by prime numbers. For a multiplicative arithmetic function and in a half-plane of absolute convergence,