Extended inverse theorems for $h$-fold sumsets in integers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914635817418752 |
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| author | Mohan Pandey, Ram Krishna |
| author_facet | Mohan Pandey, Ram Krishna |
| contents | Let $h \geq 2$, $k \geq 5$ be integers and $A$ be a nonempty finite set of $k$ integers. Very recently, Tang and Xing studied extended inverse theorems for $hk-h+1 < \left|hA\right| \leq hk+2h-3$. In this paper, we extend the work of Tang and Xing and study all possible inverse theorems for $hk-h+1<\left|hA\right| \leq hk+3h-4$. Furthermore, we give a range of $|hA|$ for which inverse problems are not possible. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_04699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extended inverse theorems for $h$-fold sumsets in integers Mohan Pandey, Ram Krishna Number Theory 11970, 11B75, 11B13 Let $h \geq 2$, $k \geq 5$ be integers and $A$ be a nonempty finite set of $k$ integers. Very recently, Tang and Xing studied extended inverse theorems for $hk-h+1 < \left|hA\right| \leq hk+2h-3$. In this paper, we extend the work of Tang and Xing and study all possible inverse theorems for $hk-h+1<\left|hA\right| \leq hk+3h-4$. Furthermore, we give a range of $|hA|$ for which inverse problems are not possible. |
| title | Extended inverse theorems for $h$-fold sumsets in integers |
| topic | Number Theory 11970, 11B75, 11B13 |
| url | https://arxiv.org/abs/2401.04699 |