Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two
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arXiv
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| Format: | Preprint |
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2025
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| author | Gajek-Leonard, Rylan Lei, Antonio |
| author_facet | Gajek-Leonard, Rylan Lei, Antonio |
| contents | Fix an odd prime $p$ and let $f$ be a non-ordinary eigen-cuspform of weight $k$ and level coprime to $p$. Assuming $p>k-1$, we compute asymptotic formulas for the Iwasawa invariants of the Mazur-Tate elements attached to $f$ in terms of the corresponding invariants of the signed $p$-adic $L$-functions. By combining this with a version of mod $p$ multiplicity one, we also obtain descriptions of the $λ$-invariants of Mazur-Tate elements attached to certain higher weight modular forms with Serre weight $<p+1$, generalizing results of Pollack and Weston in the Serre weight 2 case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two Gajek-Leonard, Rylan Lei, Antonio Number Theory Primary 11R23, Secondary 11F33 Fix an odd prime $p$ and let $f$ be a non-ordinary eigen-cuspform of weight $k$ and level coprime to $p$. Assuming $p>k-1$, we compute asymptotic formulas for the Iwasawa invariants of the Mazur-Tate elements attached to $f$ in terms of the corresponding invariants of the signed $p$-adic $L$-functions. By combining this with a version of mod $p$ multiplicity one, we also obtain descriptions of the $λ$-invariants of Mazur-Tate elements attached to certain higher weight modular forms with Serre weight $<p+1$, generalizing results of Pollack and Weston in the Serre weight 2 case. |
| title | Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two |
| topic | Number Theory Primary 11R23, Secondary 11F33 |
| url | https://arxiv.org/abs/2508.11007 |