Variants of Romanoff's theorem
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914267519778816 |
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| author | Radomskii, Artyom |
| author_facet | Radomskii, Artyom |
| contents | Let $\mathcal{A}=\{a_{n}\}_{n=1}^{\infty}$ and $\mathcal{B}=\{b_{n}\}_{n=1}^{\infty}$ be two sequences of positive integers (not necessarily distinct). Under some restrictions on $\mathcal{A}$ and $\mathcal{B}$, we obtain a lower bound for a number of integers $n$ not exceeding $x$ that can be represented as a sum $n = a_i + b_j$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variants of Romanoff's theorem Radomskii, Artyom Number Theory Let $\mathcal{A}=\{a_{n}\}_{n=1}^{\infty}$ and $\mathcal{B}=\{b_{n}\}_{n=1}^{\infty}$ be two sequences of positive integers (not necessarily distinct). Under some restrictions on $\mathcal{A}$ and $\mathcal{B}$, we obtain a lower bound for a number of integers $n$ not exceeding $x$ that can be represented as a sum $n = a_i + b_j$. |
| title | Variants of Romanoff's theorem |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.09954 |