论文标题
以杰出的玛刺形式
On Exceptional Maass Forms
论文作者
论文摘要
我们证明了$ \ gl_2（\ mathbb {a} _ {\ mathbb {q}}）$在有限和阿基米德园的cuspidal表示的satake参数之间的某些关系。因此，我们表明，Ramanujan-Petersson在固定的Prime $ p \ nmid n $中的猜想，用于\ textit {non-exceptional {non-exceptional}级别的$ n $的maass形式，暗示了$ p $的猜想，以\ textit {alld}级别的级别$ n $ and Selberg的$ 1/4 $ -4 $ -E-eigeNvalue contiment {All} Maass形式。作为一个应用程序，我们将Kim和Sarnak的$ 7/64 $折叠量用于Satake参数，所有$ p \ nmid n $用于特殊的Maass表格。
We prove certain relations between Satake parameters of cuspidal representations of $\GL_2(\mathbb{A}_{\mathbb{Q}})$ at finite and archimedean places. Consequently, we show that the Ramanujan-Petersson conjecture at a fixed prime $p\nmid N$ for \textit{non-exceptional} Maass forms of level $N$ implies the conjecture at $p$ for \textit{all} Maass forms of level $N$ and the Selberg's $1/4$-eigenvalue conjecture simultaneously. As an application, we improve Kim and Sarnak's $7/64$-bound towards the Satake parameters at all $p\nmid N$ for exceptional Maass forms.
