2 papers
math.CA2024
A general quantified Ingham-Karamata Tauberian theorem
Gregory Debruyne
We provide a general quantified Ingham-Karamata Tauberian theorem with a flexible one-sided Tauberian condition under several types of boundary behavior for the Laplace transform.…
math.NT2024
The prime number theorem through one-sided Tauberian theorems
Gregory Debruyne
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theor…