Density versions of the binary Goldbach problem
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929505458716672 |
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| author | Alsetri, Ali Shao, Xuancheng |
| author_facet | Alsetri, Ali Shao, Xuancheng |
| contents | Let $δ> 1/2$. We prove that if $A$ is a subset of the primes such that the relative density of $A$ in every reduced residue class is at least $δ$, then almost all even integers can be written as the sum of two primes in $A$. The constant $1/2$ in the statement is best possible. Moreover we give an example to show that for any $\varepsilon > 0$ there exists a subset of the primes with relative density at least $1 - \varepsilon$ such that $A+A$ misses a positive proportion of even integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18576 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density versions of the binary Goldbach problem Alsetri, Ali Shao, Xuancheng Number Theory Let $δ> 1/2$. We prove that if $A$ is a subset of the primes such that the relative density of $A$ in every reduced residue class is at least $δ$, then almost all even integers can be written as the sum of two primes in $A$. The constant $1/2$ in the statement is best possible. Moreover we give an example to show that for any $\varepsilon > 0$ there exists a subset of the primes with relative density at least $1 - \varepsilon$ such that $A+A$ misses a positive proportion of even integers. |
| title | Density versions of the binary Goldbach problem |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.18576 |