论文标题
在lang - totter猜想的siegel模块化形式
On the Lang--Trotter conjecture for Siegel modular forms
论文作者
论文摘要
令$ f $为两个cuspidal siegel模块化特征。我们证明了与$ f $相关的GALOIS表示系统的Adelic开放图像定理，从而概括了Ribet和Momose的椭圆形模块形式的结果。使用此结果，我们调查了$ f $的Hecke eigenvalues $ a_p $ a_p $ a_p $ a_p $ f $，并为固定的$ a \ in \ mathbf {c} $的固定$ a \ a \ a_p = a \} $的尺寸获得上限。
Let $f$ be a genus two cuspidal Siegel modular eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated to $f$, generalising the results of Ribet and Momose for elliptic modular forms. Using this result, we investigate the distribution of the Hecke eigenvalues $a_p$ of $f$, and obtain upper bounds for the sizes of the sets $\{p \le x : a_p = a\}$ for fixed $a\in\mathbf{C}$, in the spirit of the Lang--Trotter conjecture for elliptic curves.
