Some examples in the theory of Beurling's generalized prime numbers
Gregory Debruyne, Jan-Christoph Schlage-Puchta, Jasson Vindas
TL;DR
This paper constructs various examples of Beurling generalized prime systems to compare different conditions related to the prime number theorem in this generalized setting.
Contribution
It provides explicit examples of generalized number systems to analyze the validity of prime number theorem conditions in Beurling's framework.
Findings
Examples illustrating the failure or success of prime number theorem conditions
Comparison of different conditions in the literature
Insights into the structure of generalized prime systems
Abstract
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
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