Digitally Restricted Sets and the Goldbach Conjecture: An Exceptional Set Result
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914677272870912 |
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| author | Cumberbatch, James |
| author_facet | Cumberbatch, James |
| contents | We show that for any set $D$ of at least two digits in a given base $b$, there exists a $δ(D,b)>0$ such that within the set $\mathcal{A}$ of numbers whose digits base $b$ are exclusively from $D$, the number of even integers in $\mathcal{A}$ which are less than $X$ and not representable as the sum of two primes is less than $|\mathcal{A}(X)|^{1-δ}$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Digitally Restricted Sets and the Goldbach Conjecture: An Exceptional Set Result Cumberbatch, James Number Theory 11P32 We show that for any set $D$ of at least two digits in a given base $b$, there exists a $δ(D,b)>0$ such that within the set $\mathcal{A}$ of numbers whose digits base $b$ are exclusively from $D$, the number of even integers in $\mathcal{A}$ which are less than $X$ and not representable as the sum of two primes is less than $|\mathcal{A}(X)|^{1-δ}$ |
| title | Digitally Restricted Sets and the Goldbach Conjecture: An Exceptional Set Result |
| topic | Number Theory 11P32 |
| url | https://arxiv.org/abs/2402.07921 |