Values of algebraic functions at Liouville numbers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913143105519616 |
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| author | Bilu, Yuri Marques, Diego |
| author_facet | Bilu, Yuri Marques, Diego |
| contents | In 1953 LeVeque proved the existence of $U_m$-numbers by showing that for some specially defined Liouville number $λ$, the $m$th root $λ^{1/m}$ is in $U_m$. In this article we study the following question: let $u$ be an algebraic function of degree $m$ and $λ$ a Liouville number; under which conditions is $u(λ)$ a $U_m$-number? We consider a more refined notion of $\mathcal{L}$-numbers, and show that, under very general assumptions, an algebraic function of degree $m$ takes $U_m$-values at all $\mathcal{L}$-numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08818 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Values of algebraic functions at Liouville numbers Bilu, Yuri Marques, Diego Number Theory In 1953 LeVeque proved the existence of $U_m$-numbers by showing that for some specially defined Liouville number $λ$, the $m$th root $λ^{1/m}$ is in $U_m$. In this article we study the following question: let $u$ be an algebraic function of degree $m$ and $λ$ a Liouville number; under which conditions is $u(λ)$ a $U_m$-number? We consider a more refined notion of $\mathcal{L}$-numbers, and show that, under very general assumptions, an algebraic function of degree $m$ takes $U_m$-values at all $\mathcal{L}$-numbers. |
| title | Values of algebraic functions at Liouville numbers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.08818 |