A remark on the existence of equivariant functions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917730502836224 |
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| author | Sugiyama, Shingo |
| author_facet | Sugiyama, Shingo |
| contents | Let $Γ$ be a Fuchsian group in ${\rm SL}_2(\mathbb{R})$. In this note, we discuss the existence of $ρ$-equivariant functions for a two-dimensional representation $ρ$ of $Γ$. This assertion was first stated by Saber and Sebbar in 2020, and this note partially fills a gap of their statement by proving the assertion for a certain class of Fuchsian groups such as conjugates of subgroups of ${\rm SL}_2(\mathbb{Z})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08490 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A remark on the existence of equivariant functions Sugiyama, Shingo Number Theory Classical Analysis and ODEs Complex Variables 11F03 (Primary), 34M05, 11F12 (Secondary) Let $Γ$ be a Fuchsian group in ${\rm SL}_2(\mathbb{R})$. In this note, we discuss the existence of $ρ$-equivariant functions for a two-dimensional representation $ρ$ of $Γ$. This assertion was first stated by Saber and Sebbar in 2020, and this note partially fills a gap of their statement by proving the assertion for a certain class of Fuchsian groups such as conjugates of subgroups of ${\rm SL}_2(\mathbb{Z})$. |
| title | A remark on the existence of equivariant functions |
| topic | Number Theory Classical Analysis and ODEs Complex Variables 11F03 (Primary), 34M05, 11F12 (Secondary) |
| url | https://arxiv.org/abs/2205.08490 |