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math.NT2024
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…
math.NT2024
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…
math.NT2024
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}(Ï,…