On the estimate $M(x)=o(x)$ for Beurling generalized numbers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909643549179904 |
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| author | Vindas, Jasson |
| author_facet | Vindas, Jasson |
| contents | We show that the sum function of the Möbius function of a Beurling number system must satisfy the asymptotic bound $M(x)=o(x)$ if it satisfies the prime number theorem and its prime distribution function arises from a monotone perturbation of either the classical prime numbers or the logarithmic integral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the estimate $M(x)=o(x)$ for Beurling generalized numbers Vindas, Jasson Number Theory 11N80 We show that the sum function of the Möbius function of a Beurling number system must satisfy the asymptotic bound $M(x)=o(x)$ if it satisfies the prime number theorem and its prime distribution function arises from a monotone perturbation of either the classical prime numbers or the logarithmic integral. |
| title | On the estimate $M(x)=o(x)$ for Beurling generalized numbers |
| topic | Number Theory 11N80 |
| url | https://arxiv.org/abs/2406.00736 |