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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.NT2020
Beurling numbers whose number of prime factors lies in a specified residue class
Gregory Debruyne
We find asymptotics for , the number of positive integers below whose number of prime factors is . We study this question in the context of B…
math.NT2019
Halász's theorem for Beurling generalized numbers
Gregory Debruyne, Frederick Maes, Jasson Vindas
We show that Halász's theorem holds for Beurling numbers under the following two mild hypotheses on the generalized number system: existence of a positive density for the generaliz…