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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.18419 |
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| _version_ | 1866916773469618176 |
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| author | Clayton, Archer Dai, Helen Ni, Tianyu Ross, Erick Xue, Hui Zummo, Jake |
| author_facet | Clayton, Archer Dai, Helen Ni, Tianyu Ross, Erick Xue, Hui Zummo, Jake |
| contents | Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(Γ_0(N))$ of cuspidal modular forms of weight $2k$ and level $N$. In this paper, we study the non-repetition of the second coefficient of the characteristic polynomial of $T_m(N,2k)$. We obtain results in the horizontal aspect (where $m$ varies), the vertical aspect (where $k$ varies), and the level aspect (where $N$ varies). Finally, we use these non-repetition results to extend a result of Vilardi and Xue on distinguishing Hecke eigenforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18419 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-repetition of second coefficients of Hecke polynomials Clayton, Archer Dai, Helen Ni, Tianyu Ross, Erick Xue, Hui Zummo, Jake Number Theory 11F25 (Primary) 11F72, 11F11 (Secondary) Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(Γ_0(N))$ of cuspidal modular forms of weight $2k$ and level $N$. In this paper, we study the non-repetition of the second coefficient of the characteristic polynomial of $T_m(N,2k)$. We obtain results in the horizontal aspect (where $m$ varies), the vertical aspect (where $k$ varies), and the level aspect (where $N$ varies). Finally, we use these non-repetition results to extend a result of Vilardi and Xue on distinguishing Hecke eigenforms. |
| title | Non-repetition of second coefficients of Hecke polynomials |
| topic | Number Theory 11F25 (Primary) 11F72, 11F11 (Secondary) |
| url | https://arxiv.org/abs/2411.18419 |