Intersections of sumsets in additive number theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916012360728576 |
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| author | Nathanson, Melvyn B. |
| author_facet | Nathanson, Melvyn B. |
| contents | Let $A$ be a subset of an additive abelian semigroup $S$ and let $hA$ be the $h$-fold sumset of $A$. The following question is considered: Let $(A_q)_{q=1}^{\infty}$ be a strictly decreasing sequence of sets in $S$ and let $A = \bigcap_{q=1}^{\infty} A_q$. When does one have \[ hA = \bigcap_{q=1}^{\infty} hA_q \] for some or all $h \geq 2$? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersections of sumsets in additive number theory Nathanson, Melvyn B. Number Theory 11B13, 11B05, 11B75, 11P70, 22D99 Let $A$ be a subset of an additive abelian semigroup $S$ and let $hA$ be the $h$-fold sumset of $A$. The following question is considered: Let $(A_q)_{q=1}^{\infty}$ be a strictly decreasing sequence of sets in $S$ and let $A = \bigcap_{q=1}^{\infty} A_q$. When does one have \[ hA = \bigcap_{q=1}^{\infty} hA_q \] for some or all $h \geq 2$? |
| title | Intersections of sumsets in additive number theory |
| topic | Number Theory 11B13, 11B05, 11B75, 11P70, 22D99 |
| url | https://arxiv.org/abs/2512.23574 |