论文标题
在siegel eigenforms的Hecke特征值的迹象上
On signs of Hecke eigenvalues of Siegel eigenforms
论文作者
论文摘要
在本文中，我们将整体群体上第二学位的cuspidal特征形式与他们的hecke特征值的符号区分开。为了建立我们的定理，我们获得了两个siegel特征形式的特征值的同时符号变化的结果。在证据的过程中，我们还证明了两个不同的siegel特征形式的satake $ p $ - 参数与密度的一组素数$ p $ 1不同。证明后者结果的主要成分是siegel eigenforms附加的Galois表示理论。
In this article, we distinguish Siegel cuspidal eigenforms of degree two on the full symplectic group from the signs of their Hecke eigenvalues. To establish our theorem, we obtain a result towards simultaneous sign changes of eigenvalues of two Siegel eigenforms. In the course of the proof, we also prove that the Satake $p$-parameters of two different Siegel eigenforms are distinct for a set of primes $p$ of density 1. The main ingredient to prove the latter result is the theory of Galois representations attached to Siegel eigenforms.
