16 citations · 58 across the 16 of their papers we have counts for
4 papers · 1 filter
Note on a conjecture of Bateman and Diamond concerning the abstract PNT with Malliavin-type remainder
Frederik Broucke
Given , we show the existence of a Beurling generalized number system whose integer counting satisfies for some and $c…
Beurling integers with RH and large oscillation
Frederik Broucke, Gregory Debruyne, Jasson Vindas
We construct a Beurling generalized number system satisfying the Riemann hypothesis and whose integer counting function displays extremal oscillation in the following sense. The pr…
An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions
Frederik Broucke, Gregory Debruyne, Jasson Vindas
We study the family of Fourier-Laplace transforms $$ F_{α,β}(z)= \operatorname*{F.p.} \int_{0}^{\infty} t^β\exp(\mathrm{i} t^α-\mathrm{i} z t)\:\mathrm{d} t, \quad \operatorname*{I…
On the absence of remainders in the Wiener-Ikehara and Ingham-Karamata theorems: a constructive approach
Frederik Broucke, Gregory Debruyne, Jasson Vindas
We construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata the…