Additive decompositions of large multiplicative subgroups in finite fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911870798004224 |
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| author | Yip, Chi Hoi |
| author_facet | Yip, Chi Hoi |
| contents | We show that a large multiplicative subgroup of a finite field $\mathbb{F}_q$ cannot be decomposed into $A+A$ or $A+B+C$ nontrivially. We also find new families of multiplicative subgroups that cannot be decomposed as the sum of two sets nontrivially. In particular, our results extensively generalize the results of Sárközy and Shkredov on the additive decomposition of the set of quadratic residues modulo a prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13801 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Additive decompositions of large multiplicative subgroups in finite fields Yip, Chi Hoi Number Theory 11B13, 11B30, 11P70, 11T06 We show that a large multiplicative subgroup of a finite field $\mathbb{F}_q$ cannot be decomposed into $A+A$ or $A+B+C$ nontrivially. We also find new families of multiplicative subgroups that cannot be decomposed as the sum of two sets nontrivially. In particular, our results extensively generalize the results of Sárközy and Shkredov on the additive decomposition of the set of quadratic residues modulo a prime. |
| title | Additive decompositions of large multiplicative subgroups in finite fields |
| topic | Number Theory 11B13, 11B30, 11P70, 11T06 |
| url | https://arxiv.org/abs/2304.13801 |