Structure theory of set addition with two operations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909994258006016 |
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| author | Semchankau, Aliaksei Shkredov, Ilya |
| author_facet | Semchankau, Aliaksei Shkredov, Ilya |
| contents | We take the first step toward a structure theory that includes both operations of a ring $\mathcal{R}$. More precisely, we prove a series of inverse results for the structure of sets $A\subseteq \mathbf{F}_p$ such that, under certain conditions on integers $r_1, \dots, r_k$, one has $|A^{r_1} + \dots + A^{r_k}| \ll \sqrt[k]{p^{k-1} |A|}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12457 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structure theory of set addition with two operations Semchankau, Aliaksei Shkredov, Ilya Combinatorics Number Theory We take the first step toward a structure theory that includes both operations of a ring $\mathcal{R}$. More precisely, we prove a series of inverse results for the structure of sets $A\subseteq \mathbf{F}_p$ such that, under certain conditions on integers $r_1, \dots, r_k$, one has $|A^{r_1} + \dots + A^{r_k}| \ll \sqrt[k]{p^{k-1} |A|}$. |
| title | Structure theory of set addition with two operations |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2601.12457 |