2 papers
math.NT2020
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…
math.CV2020
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…