Maps preserving the sum-to-difference ratio in characteristic $p$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911079586594816 |
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| author | Chebolu, Sunil Khare, Apoorva Sen, Anindya |
| author_facet | Chebolu, Sunil Khare, Apoorva Sen, Anindya |
| contents | Given a field $\mathbb{F}$, we introduce a novel group $SD(\mathbb{F})$ of its self-maps: the solutions $f \colon \mathbb{F} \twoheadrightarrow \mathbb{F}$ to the functional equation $f \left( (x+y)/(x-y) \right) = (f(x) + f(y))/(f(x) - f(y))$ for all $ x \neq y$ in $\mathbb{F}$. We compute this group for all fields algebraic over $\mathbb{F}_p$. In particular, this group distinguishes $\mathbb{F}_5$ among all finite fields $\mathbb{F}_q$, and in fact among all subfields of $\overline{\mathbb{F}_q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maps preserving the sum-to-difference ratio in characteristic $p$ Chebolu, Sunil Khare, Apoorva Sen, Anindya Number Theory Commutative Algebra Rings and Algebras 11T06, 12E12, 12F05 (primary), 12E20 (secondary) Given a field $\mathbb{F}$, we introduce a novel group $SD(\mathbb{F})$ of its self-maps: the solutions $f \colon \mathbb{F} \twoheadrightarrow \mathbb{F}$ to the functional equation $f \left( (x+y)/(x-y) \right) = (f(x) + f(y))/(f(x) - f(y))$ for all $ x \neq y$ in $\mathbb{F}$. We compute this group for all fields algebraic over $\mathbb{F}_p$. In particular, this group distinguishes $\mathbb{F}_5$ among all finite fields $\mathbb{F}_q$, and in fact among all subfields of $\overline{\mathbb{F}_q}$. |
| title | Maps preserving the sum-to-difference ratio in characteristic $p$ |
| topic | Number Theory Commutative Algebra Rings and Algebras 11T06, 12E12, 12F05 (primary), 12E20 (secondary) |
| url | https://arxiv.org/abs/2507.20604 |