Recent progress on the Selberg-Delange method in analytic number theory

Abstract: 

Let ϱ be a complex number and let f be a multiplicative arithmetic function whose Dirichlet series takes the form ζ(s)ϱG(s), where ζ(s) is the Riemann zeta function and 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 shall recall these statements and briefly describe the proofs. The main part of of the lecture will be devoted to give an account on recent works (in particular a joint paper with Régis de la Bretèche) considering different set of hypotheses, not directly comparable to the previous ones. We shall investigate what assumptions are sufficient to yield  sharp  asymptotic estimates for the averages of f. This talk is part of the online Number Theory Web Seminar, and will be streamed live on Zoom. To attend the talks, registration is necessary. To register please visit our website www.ntwebseminar.org/home Registered users will receive an email before each talk with a link to the Zoom meeting.

Organisers: Mike Bennett (University of British Columbia) Philipp Habegger (University of Basel) Alina Ostafe (UNSW Sydney)