16 citations · 58 across the 16 of their papers we have counts for
17 papers
On a question of Gowers related to Littlewood's conjecture
Frederik Broucke, Máté Matolcsi, Szilárd Gy. Révész
In a blogpost in 2009, Gowers raised a possible approach to Littlewood's conjecture in Diophantine approximation, leading to a question about the existence of sufficiently many poi…
On the connection between zero-free regions and the error term in the Prime Number Theorem
Frederik Broucke
We provide for a wide class of zero-free regions an upper bound for the error term in the Prime Number Theorem, refining works of Pintz (1980), Johnston (2024), and Révész (2024).…
On zero-density estimates for Beurling zeta functions
Frederik Broucke
We show the zero-density estimate \[ N(ζ_{\mathcal{P}}; α, T) \ll T^{\frac{4(1-α)}{3-2α-θ}}(\log T)^{9} \] for Beurling zeta functions attached to Beurling genera…
A Mean Value Theorem for general Dirichlet Series
Frederik Broucke, Titus Hilberdink
In this paper we obtain a mean value theorem for a general Dirichlet series with positive coefficients for which the counting function $A(x)…
Some examples of well-behaved Beurling number systems
Frederik Broucke, Gregory Debruyne, Szilárd Révész
We investigate the existence of well-behaved Beurling number systems, which are systems of Beurling generalized primes and integers which admit a power saving in the error term of…
On the Lindelöf hypothesis for general sequences
Frederik Broucke, Sebastian Weishäupl
In a recent paper, Gonek, Graham, and Lee introduced a notion of the Lindelöf hypothesis (LH) for general sequences which coincides with the usual Lindelöf hypothesis for the Riema…
A note on Bohr's theorem for Beurling integer systems
Frederik Broucke, Athanasios Kouroupis, Karl-Mikael Perfekt
Given a sequence of frequencies , a corresponding generalized Dirichlet series is of the form . We are interested in multiplicati…
On zero-density estimates and the PNT in short intervals for Beurling generalized numbers
Frederik Broucke, Gregory Debruyne
We study the distribution of zeros of zeta functions associated to Beurling generalized prime number systems whose integers are distributed as . We obtain in pa…
Distributed-order time-fractional wave equations
Frederik Broucke, Ljubica Oparnica
Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through co…
The optimal Malliavin-type remainder for Beurling generalized integers
Frederik Broucke, Gregory Debruyne, Jasson Vindas
We establish the optimal order of Malliavin-type remainders in the asymptotic density approximation formula for Beurling generalized integers. Given and (with $c…
The pointwise behavior of Riemann's function
Frederik Broucke, Jasson Vindas
We present a new and simple method for the determination of the pointwise Hölder exponent of Riemann's function at every point of the rea…
Micro-local and qualitative analysis of the fractional Zener wave equation
Frederik Broucke, Ljubica Oparnica
This paper concerns the micro-local and qualitative analysis of the fractional Zener wave equation. The classical and Gevrey-type wave front sets of the fundamental solution are de…
A new generalized prime random approximation procedure and some of its applications
Frederik Broucke, Jasson Vindas
We present a new random approximation method that yields the existence of a discrete Beurling prime system which is very close in a certain p…
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…