Sums of dilates over groups of prime order
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914957130465280 |
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| author | Conlon, David Lim, Jeck |
| author_facet | Conlon, David Lim, Jeck |
| contents | For $p$ prime, $A \subseteq \mathbb{Z}/p\mathbb{Z}$ and $λ\in \mathbb{Z}$, the sum of dilates $A + λ\cdot A$ is defined by \[A + λ\cdot A = \{a + λa' : a, a' \in A\}.\] The basic problem on such sums of dilates asks for the minimum size of $|A + λ\cdot A|$ for given $λ$, $A$ of given density $α$, and $p$ tending to infinity. We investigate this problem for $α$ fixed and $λ$ tending to infinity, proving near-optimal bounds in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sums of dilates over groups of prime order Conlon, David Lim, Jeck Combinatorics Number Theory 05D99, 11B13, 11B75 For $p$ prime, $A \subseteq \mathbb{Z}/p\mathbb{Z}$ and $λ\in \mathbb{Z}$, the sum of dilates $A + λ\cdot A$ is defined by \[A + λ\cdot A = \{a + λa' : a, a' \in A\}.\] The basic problem on such sums of dilates asks for the minimum size of $|A + λ\cdot A|$ for given $λ$, $A$ of given density $α$, and $p$ tending to infinity. We investigate this problem for $α$ fixed and $λ$ tending to infinity, proving near-optimal bounds in this case. |
| title | Sums of dilates over groups of prime order |
| topic | Combinatorics Number Theory 05D99, 11B13, 11B75 |
| url | https://arxiv.org/abs/2409.17112 |