Identical representation functions of linear forms
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908393304752128 |
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| author | Kiss, Sándor Sándor, Csaba |
| author_facet | Kiss, Sándor Sándor, Csaba |
| contents | For a set of natural numbers $A$, let $R_{A}(n)$ be the number of representations of a natural number $n$ as the sum of two terms from $A$. Many years ago, Nathanson studied the conditions for the set $A$ and $B$ of natural numbers that are needed to guarantee that $R_{A}(n) = R_{B}(n)$ for every positive integer $n$. In the last decades, similar questions have been studied by many authors. In this paper, we extend Nathanson's result to representation functions associated to linear forms and we study related problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identical representation functions of linear forms Kiss, Sándor Sándor, Csaba Number Theory For a set of natural numbers $A$, let $R_{A}(n)$ be the number of representations of a natural number $n$ as the sum of two terms from $A$. Many years ago, Nathanson studied the conditions for the set $A$ and $B$ of natural numbers that are needed to guarantee that $R_{A}(n) = R_{B}(n)$ for every positive integer $n$. In the last decades, similar questions have been studied by many authors. In this paper, we extend Nathanson's result to representation functions associated to linear forms and we study related problems. |
| title | Identical representation functions of linear forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.03983 |