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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2602.22471 |
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| _version_ | 1866911469612826624 |
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| author | Matsuda, Kazuhide |
| author_facet | Matsuda, Kazuhide |
| contents | In this paper, we introduce higher level versions of the theta group $Γ_θ.$ In particular, we treat level 3 and 4 versions of the theta group, $Γ_{θ,3}$ and $Γ_{θ,4}$ and prove that $\displaystyle F(τ)=η\left(\frac{τ-1}{3} \right) η\left(\frac{τ+1}{3} \right)$ and $\displaystyle G(τ)=η\left(\frac{τ-1}{4} \right) η\left(\frac{τ+1}{4} \right)$ are modular forms on $Γ_{θ,3}$ and $Γ_{θ,4}$ respectively. Moreover we compute their multiplier systems, $ν_{F}$ and $ν_{G}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22471 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analogue of the theta group $Γ_θ$ Matsuda, Kazuhide Number Theory 14K25, 11E25 In this paper, we introduce higher level versions of the theta group $Γ_θ.$ In particular, we treat level 3 and 4 versions of the theta group, $Γ_{θ,3}$ and $Γ_{θ,4}$ and prove that $\displaystyle F(τ)=η\left(\frac{τ-1}{3} \right) η\left(\frac{τ+1}{3} \right)$ and $\displaystyle G(τ)=η\left(\frac{τ-1}{4} \right) η\left(\frac{τ+1}{4} \right)$ are modular forms on $Γ_{θ,3}$ and $Γ_{θ,4}$ respectively. Moreover we compute their multiplier systems, $ν_{F}$ and $ν_{G}$. |
| title | Analogue of the theta group $Γ_θ$ |
| topic | Number Theory 14K25, 11E25 |
| url | https://arxiv.org/abs/2602.22471 |