Non-repetition of second coefficients of Hecke polynomials
| Autor: | Clayton, Archer, Dai, Helen, Ni, Tianyu, Ross, Erick, Xue, Hui, Zummo, Jake |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(\Gamma_0(N))$ 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. Comment: 22 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|