A simple proof of the Wiener–Ikehara Tauberian theorem

Speaker: Jagannath Sahoo

Date: Wed, Jun 19, 2024

Location: PIMS, University of British Columbia

Conference: Comparative Prime Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory


The Wiener–Ikehara Tauberian theorem is an important theorem giving an asymptotic formula for the sum of coefficients of a Dirichlet series. In this talk, we present a simple and elegant proof of the Wiener–Ikehara Tauberian theorem which relies only on basic Fourier analysis and known estimates for the given Dirichlet series. This method allows us to derive a version of the WienerIkehara theorem with an error term. This is joint work with Prof. M. Ram Murty and Prof. Akshaa Vatwani.

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