Newton Polygons of Hecke Operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866910217463136256 |
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| author | Chiriac, Liubomir Jorza, Andrei |
| author_facet | Chiriac, Liubomir Jorza, Andrei |
| contents | In this computational paper we verify a truncated version of the Buzzard-Calegari conjecture on the Newton polygon of the Hecke operator $T_2$ for all large enough weights. We first develop a formula for computing $p$-adic valuations of exponential sums, which we then implement to compute $2$-adic valuations of traces of Hecke operators acting on spaces of cusp forms. Finally, we verify that if Newton polygon of the Buzzard-Calegari polynomial has a vertex at $n\leq 15$, then it agrees with the Newton polygon of $T_2$ up to $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_02909 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Newton Polygons of Hecke Operators Chiriac, Liubomir Jorza, Andrei Number Theory In this computational paper we verify a truncated version of the Buzzard-Calegari conjecture on the Newton polygon of the Hecke operator $T_2$ for all large enough weights. We first develop a formula for computing $p$-adic valuations of exponential sums, which we then implement to compute $2$-adic valuations of traces of Hecke operators acting on spaces of cusp forms. Finally, we verify that if Newton polygon of the Buzzard-Calegari polynomial has a vertex at $n\leq 15$, then it agrees with the Newton polygon of $T_2$ up to $n$. |
| title | Newton Polygons of Hecke Operators |
| topic | Number Theory |
| url | https://arxiv.org/abs/1912.02909 |