Supersingular loci from traces of Hecke operators
| العنوان: | Supersingular loci from traces of Hecke operators |
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| المؤلفون: | Kevin Gomez, Kaya Lakein, Anne Larsen |
| المصدر: | Proceedings of the American Mathematical Society. 151:511-525 |
| بيانات النشر: | American Mathematical Society (AMS), 2022. |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Mathematics - Number Theory, Applied Mathematics, General Mathematics, FOS: Mathematics, Number Theory (math.NT), 11F33, 11G07 |
| الوصف: | A classical observation of Deligne shows that, for any prime $p \geq 5$, the divisor polynomial of the Eisenstein series $E_{p-1}(z)$ mod $p$ is closely related to the supersingular polynomial at $p$, $$S_p(x) := \prod_{E/\bar{\mathbb{F}}_p \text{ supersingular}}(x-j(E)) \in \mathbb{F}_p[x].$$ Deuring, Hasse, and Kaneko and Zagier found other families of modular forms which also give the supersingular polynomial at $p$. In a new approach, we prove an analogue of Deligne's result for the Hecke trace forms $T_k(z)$ defined by the Hecke action on the space of cusp forms $S_k$. We use the Eichler-Selberg trace formula to identify congruences between trace forms of different weights mod $p$, and then relate their divisor polynomials to $S_p(x)$ using Deligne's observation. Minor revisions addressing a referee's comments |
| تدمد: | 1088-6826 0002-9939 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6daa923ca1dee98885f909da779c3a38 https://doi.org/10.1090/proc/16148 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....6daa923ca1dee98885f909da779c3a38 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 10886826 00029939 |
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