17 citations · 118 across the 21 of their papers we have counts for
5 papers · 1 filter
Generalization of the Wiener-Ikehara theorem
Gregory Debruyne, Jasson Vindas
We study the Wiener-Ikehara theorem under the so-called log-linearly slowly decreasing condition. Moreover, we clarify the connection between two different hypotheses on the Laplac…
Estimates for Beurling numbers
Gregory Debruyne, Harold G. Diamond, Jasson Vindas
In classical prime number theory there are several asymptotic formulas said to be "equivalent" to the PNT. One is the bound for the sum function of the Moebius functi…
On PNT equivalences for Beurling numbers
Gregory Debruyne, Jasson Vindas
In classical prime number theory several asymptotic relations are considered to be "equivalent" to the prime number theorem. In the setting of Beurling generalized numbers, this ma…
Complex Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior
Gregory Debruyne, Jasson Vindas
We provide several Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior. Our results generalize and improve various known versions of the Ingham-Fa…
On General Prime Number Theorems with Remainder
Gregory Debruyne, Jasson Vindas
We show that for Beurling generalized numbers the prime number theorem in remainder form $$π(x) = \operatorname*{Li}(x) + O\left(\frac{x}{\log^{n}x}\right) \quad \mbox{for all } n\…