Abstract
A famous theorem of Wiener states the conditions under which the reciprocal of a function with an absolutely convergent Fourier series also has an absolutely convergent Fourier series. We offer an elementary proof of the fact, first proven in [2], that if $F(s)$ has an absolutely convergent Dirichlet series then $1/F(s)$ has an absolutely convergent Dirichlet series if and only if $\left | {F(s)} \right |$ is bounded away from zero in the closed right half-plane.
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