2012/10/08 by Szilárd Gy. Révész, Révész, Szilárd Gy., Anne de Roton +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Stochastic processes and financial applications #math.NT
paper · pdf · doi:10.48550/arxiv.1210.2284
arxiv created 2012/10/08 · openalex publication_date 2012/10/08 · arxiv updated 2012/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the classical Wiener-Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener-Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generalality. The crux of the proof is a proper, asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener-Ikehara Theorem.