Remarks on the Selberg–Delange method (joint work with Gerald Tenenbaum) by Regis de la Bretèche

Speaker: R ́egis de la Bret`eche

Title: Remarks on the Selberg–Delange method (joint work with Ger-
ald Tenenbaum)

Abstract: Let % be a complex number and let f be a multiplicative
arithmetic function whose Dirichlet series takes the form ζ(s)
%G(s),
where G is associated to a multiplicative function g. The classical

Selberg-Delange method furnishes asymptotic estimates for the aver-
ages 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.