论文标题
2度和导体1的L功能分类
Classification of L-functions of degree 2 and conductor 1
论文作者
论文摘要
我们在Extended Selberg类的一般框架中对2度2的功能和指挥1进行了完整描述。这是通过新的数值不变$χ_f$执行的，该数值不变$χ_f$很容易从功能方程的数据中计算出来。我们表明，$χ_f$的价值对$ f $的性质进行了精确描述，从而提供了Hecke和Maass的经典匡威定理的鲜明形式。特别是，我们的结果证实，在所考虑的特殊情况下，Selberg类中的功能是自动形态$ L $功能的猜想。
We give a full description of the functions $F$ of degree 2 and conductor 1 in the general framework of the extended Selberg class. This is performed by means of a new numerical invariant $χ_F$, which is easily computed from the data of the functional equation. We show that the value of $χ_F$ gives a precise description of the nature of $F$, thus providing a sharp form of the classical converse theorems of Hecke and Maass. In particular, our result confirms, in the special case under consideration, the conjecture that the functions in the Selberg class are automorphic $L$-functions.
