See Dirichlet series on Wiktionary
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"text": "2014, Marius Overholt, A Course in Analytic Number Theory, American Mathematical Society, page 157,\nThe sum\nA(s)=∑ₙ₌₁ ᪲a_nn⁻ˢ\nof a convergent Dirichlet series is a holomorphic (single-valued analytic) function in the half plane σ>σ_c(A), and the terms of the Dirichlet series are holomorphic in the whole complex plane, and the series converges uniformly on every compact subset of σ>σ_c(A) by Proposition 3.3."
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