From the 1 of 6 linked papers with an AI index.
6 papers
On a question of Gowers related to Littlewood's conjecture
Frederik Broucke, Máté Matolcsi, Szilárd Gy. Révész
The authors construct explicitly many points in the unit cube whose pairwise hyperbolic distances are large, answering a question posed by Gowers and showing that his proposed appr…
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…
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…
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…