Definability of complex functions in o-minimal structures
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908412539830272 |
|---|---|
| author | Padgett, Adele Speissegger, Patrick |
| author_facet | Padgett, Adele Speissegger, Patrick |
| contents | We prove that some holomorphic continuations of functions in the classes $\mathbf{an}^*$ and $\mathcal{G}$ are definable in the o-minimal structures $\mathbb{R}_{\mathrm{an}^*}$ and $\mathbb{R}_{\mathcal{G}}$ respectively. More specifically, we give complex domains on which the holomorphic continuations are definable, and show they are optimal. As an application, we describe optimal domains on which the Riemann $ζ$ function is definable in o-minimal expansions of $\mathbb{R}_{\mathrm{an}^*,\exp}$ and on which the $Γ$ function is definable in o-minimal expansions of $\mathbb{R}_{\mathcal{G},\exp}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Definability of complex functions in o-minimal structures Padgett, Adele Speissegger, Patrick Logic 03C64, 32D15, 03C40, 32B20 We prove that some holomorphic continuations of functions in the classes $\mathbf{an}^*$ and $\mathcal{G}$ are definable in the o-minimal structures $\mathbb{R}_{\mathrm{an}^*}$ and $\mathbb{R}_{\mathcal{G}}$ respectively. More specifically, we give complex domains on which the holomorphic continuations are definable, and show they are optimal. As an application, we describe optimal domains on which the Riemann $ζ$ function is definable in o-minimal expansions of $\mathbb{R}_{\mathrm{an}^*,\exp}$ and on which the $Γ$ function is definable in o-minimal expansions of $\mathbb{R}_{\mathcal{G},\exp}$. |
| title | Definability of complex functions in o-minimal structures |
| topic | Logic 03C64, 32D15, 03C40, 32B20 |
| url | https://arxiv.org/abs/2506.15119 |