Number of Polynomials Vanishing on a Basis of $S_m(Γ_0(N))$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911879413104640 |
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| author | Kodrnja, Iva Koncul, Helena |
| author_facet | Kodrnja, Iva Koncul, Helena |
| contents | In this paper we find the number of homogeneous polynomials of degree d such that they vanish on cuspidal modular forms of even weight $m\geq 2$ that form a basis for $S_m(Γ_0(N))$. We use these cuspidal forms to embedd $X_0(N)$ to projective space and we find the Hilbert polynomial of the graded ideal of the projective curve that is the image of this embedding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Number of Polynomials Vanishing on a Basis of $S_m(Γ_0(N))$ Kodrnja, Iva Koncul, Helena Number Theory 11F11, 05E40, 13F20 In this paper we find the number of homogeneous polynomials of degree d such that they vanish on cuspidal modular forms of even weight $m\geq 2$ that form a basis for $S_m(Γ_0(N))$. We use these cuspidal forms to embedd $X_0(N)$ to projective space and we find the Hilbert polynomial of the graded ideal of the projective curve that is the image of this embedding. |
| title | Number of Polynomials Vanishing on a Basis of $S_m(Γ_0(N))$ |
| topic | Number Theory 11F11, 05E40, 13F20 |
| url | https://arxiv.org/abs/2405.10747 |