Linear relations between $L$-values of newforms and moments of elliptic $K$ integral
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914060686065664 |
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| author | Au, Kam Cheong |
| author_facet | Au, Kam Cheong |
| contents | By systematically translating certain integrals involving moments of the elliptic integral into $L$-values of modular forms on $Γ_1(4), Γ(4)$ and $Γ_1(8)$, and then utilizing relations among the critical $L$-values of cuspidal newforms, we obtain a dimension formula for the space spanned by these integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear relations between $L$-values of newforms and moments of elliptic $K$ integral Au, Kam Cheong Number Theory Classical Analysis and ODEs 11F11, 11F67, 33C75 (Primary) 33C20 (Secondary) By systematically translating certain integrals involving moments of the elliptic integral into $L$-values of modular forms on $Γ_1(4), Γ(4)$ and $Γ_1(8)$, and then utilizing relations among the critical $L$-values of cuspidal newforms, we obtain a dimension formula for the space spanned by these integrals. |
| title | Linear relations between $L$-values of newforms and moments of elliptic $K$ integral |
| topic | Number Theory Classical Analysis and ODEs 11F11, 11F67, 33C75 (Primary) 33C20 (Secondary) |
| url | https://arxiv.org/abs/2509.19960 |