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Some examples in the theory of Beurling’s generalized prime numbers

Gregory Debruyne, Jan‐Christoph Schlage‐Puchta, Jasson Vindas

Acta Arithmetica · 2016 · 16 citations · 5 references

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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.

References

5

Asymptotic distribution of Beurling's generalized integers

Harold G. Diamond · Illinois Journal of Mathematics · 1970 · 41 citations

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A set of generalized numbers showing Beurling's theorem to be sharp

Harold G. Diamond · Illinois Journal of Mathematics · 1970 · 39 citations · Full text

, , +5

The prime number theorem for Beurling's generalized numbers

Harold G. Diamond · Journal of Number Theory · 1969 · 34 citations

, , +4

Structural theorems for quasiasymptotics of distributions at infinity

Jasson Vindas · Publications de l Institut Mathematique · 2008 · 28 citations · Full text

, , +6

The prime number theorem for Beurling's generalized numbers. New cases

Jan‐Christoph Schlage‐Puchta, Jasson Vindas · Acta Arithmetica · 2012 · 13 citations · Full text

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