论文标题
Hecke特征值的计算（mod $ p $）通过四个
Computation of Hecke eigenvalues (mod $p$) via quaternions
论文作者
论文摘要
在1987年的一封信中，塞雷证明了由mod $ $ p $模块化形式（固定级别$γ（n）$ coprime到$ p $的hecke特征值的系统和任何重量$ k $）与函数$ω（n）\ to \ bar to \ bar {\ mathbb f} $ iS $ double double double double double double double double（ （\ Mathbb a_f）$和$ d $是$ \ mathbb q $在$ \ {p，\ f，\ infty \} $上分配的唯一Quaternion代数。我们提出了一种算法，然后以组合方式在季节侧计算这些Hecke特征值。
In a 1987 letter, Serre proves that the systems of Hecke eigenvalues arising from mod $p$ modular forms (of fixed level $Γ(N)$ coprime to $p$, and any weight $k$) are the same as those arising from functions $Ω(N) \to \bar{\mathbb F}_p$, where $Ω(N)$ is some double quotient of $D^\times (\mathbb A_f)$ and $D$ is the unique quaternion algebra over $\mathbb Q$ ramified at $\{p,\infty\}$. We present an algorithm which then computes these Hecke eigenvalues on the quaternion side in a combinatorial manner.
