Remarks on the Selberg-Delange method
Résumé
Let ρ be a complex number and let f be a multiplicative arithmetic function whose Dirichlet series takes the form ζ(s)^ρ G(s), where G is associated to a multiplicative function g. The classical Selberg-Delange method furnishes asymptotic estimates for the averages of f under assumptions of either analytic continuation for G, or absolute convergence of a finite number of derivatives of G(s) at s = 1. We consider different set of hypotheses, not directly comparable to the previous ones, and investigate how they can yield sharp asymptotic estimates for the averages of f .
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