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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.08867 |
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| _version_ | 1866912148466171904 |
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| author | Tang, Jincheng Zhang, Xin |
| author_facet | Tang, Jincheng Zhang, Xin |
| contents | We obtain a bounded generation theorem over $\mathcal O/\mathfrak a$, where $\mathcal O$ is the ring of integers of a number field and $\mathfrak a$ a general ideal of $\mathcal O$. This addresses a conjecture of Salehi-Golsefidy. Along the way, we obtain nontrivial bounds for additive character sums over $\mathcal O/\mathcal P^n$ for a prime ideal $\mathcal P$ with the aid of certain sum-product estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08867 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sum-product phenomenon in quotients of rings of algebraic integers Tang, Jincheng Zhang, Xin Number Theory Combinatorics 20D60, 11T23 We obtain a bounded generation theorem over $\mathcal O/\mathfrak a$, where $\mathcal O$ is the ring of integers of a number field and $\mathfrak a$ a general ideal of $\mathcal O$. This addresses a conjecture of Salehi-Golsefidy. Along the way, we obtain nontrivial bounds for additive character sums over $\mathcal O/\mathcal P^n$ for a prime ideal $\mathcal P$ with the aid of certain sum-product estimates. |
| title | Sum-product phenomenon in quotients of rings of algebraic integers |
| topic | Number Theory Combinatorics 20D60, 11T23 |
| url | https://arxiv.org/abs/2308.08867 |