Browsing by Author "Murty, M. Ram"

The Wiener–Ikehara Tauberian theorem is an important theorem giving an asymptotic formula for the sum of coefficients of a Dirichlet series [Formula presented]. We provide 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 also allows us to derive a version of the Wiener–Ikehara theorem with an error term.

The authors would like to inform the reader that the statement of Theorem 1.1 in [1] should be modified as follows. In addition to the assumption of absolute convergence for [Formula presented]. Moreover, the conclusion of Theorem 1.1 should be modified to the following: [Formula presented] such as the one imposed by Tenenbaum [2] in his discussion of the Selberg–Delange method. The most expedient way of arriving at the asymptotic formula (without the error term) in Theorem 1.1 is to first observe that [Formula presented] respectively. Using the elementary result [Formula presented] of the above theorem, which of course is the content of the third author's paper [3]. We thank Frederik Broucke for pointing out these lacunae in our paper.