17 citations · 118 across the 21 of their papers we have counts for
23 papers
A general quantified Ingham-Karamata Tauberian theorem
Gregory Debruyne
We provide a general quantified Ingham-Karamata Tauberian theorem with a flexible one-sided Tauberian condition under several types of boundary behavior for the Laplace transform.…
The prime number theorem through one-sided Tauberian theorems
Gregory Debruyne
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theor…
On the density hypothesis for -functions associated with holomorphic cusp forms
Bin Chen, Gregory Debruyne, Jasson Vindas
We study the range of validity of the density hypothesis for the zeros of -functions associated with cusp Hecke eigenforms of even integral weight and prove that $N_{f}(σ, T…
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 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…
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…