Newform Eisenstein Congruences of Local Origin
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908860550217728 |
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| author | Fretwell, Dan Roberts, Jenny |
| author_facet | Fretwell, Dan Roberts, Jenny |
| contents | We give a general conjecture concerning the existence of Eisenstein congruences between weight $k\geq 3$ newforms of square-free level $NM$ and weight $k$ new Eisenstein series of square-free level $N$. Our conjecture allows the forms to have arbitrary character $χ$ of conductor $N$. The special cases $M=1$ and $M=p$ prime are fully proved, with partial results given in general. We also consider the relation with the Bloch-Kato conjecture, and finish with computational examples demonstrating cases of our conjecture that have resisted proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09842 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Newform Eisenstein Congruences of Local Origin Fretwell, Dan Roberts, Jenny Number Theory 11F33, 11F03, 11F30, 11F80 We give a general conjecture concerning the existence of Eisenstein congruences between weight $k\geq 3$ newforms of square-free level $NM$ and weight $k$ new Eisenstein series of square-free level $N$. Our conjecture allows the forms to have arbitrary character $χ$ of conductor $N$. The special cases $M=1$ and $M=p$ prime are fully proved, with partial results given in general. We also consider the relation with the Bloch-Kato conjecture, and finish with computational examples demonstrating cases of our conjecture that have resisted proof. |
| title | Newform Eisenstein Congruences of Local Origin |
| topic | Number Theory 11F33, 11F03, 11F30, 11F80 |
| url | https://arxiv.org/abs/2306.09842 |