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Reciprocal

The reciprocal of the zeta function may be expressed as a Dirichlet series over the Möbius function μ (n):

for every complex number s with real part greater than 1. There are a number of similar relations involving various well-known multiplicative functions; these are given in the article on the Dirichlet series.

The Riemann hypothesis is equivalent to the claim that this expression is valid when the real part of s is greater than 1 / 2.