论文标题
极端P-ADIC L功能
Extremal p-adic L-functions
论文作者
论文摘要
在本说明中，我们提出了与经典模块化尖齿特征形式相关的循环p-adic l功能的新结构。这使我们能够涵盖迄今为止的大多数已知案例，并提供了一种适合对任意组自动形式的概括的方法。在Q上GL2的经典环境中，这使我们能够在迄今未透明的极端情况下构造P-ADIC L功能，这在不太可能的假设下出现了P-Th Hecke多项式具有双根。尽管泰特的猜想意味着对于GL2/Q永远不应发生这种情况，但希尔伯特·库斯普（Hilbert Cusp）的自然界确实存在明显的概括，而不是完全实真实的偶数字段，本文提出了一种应该适应此设置的方法。我们进一步研究了这些极端P-ADIC L功能的可接受性和插值特性，并将它们与Coleman家族沿着Coleman家族的两种可变量的P-ADIC L函数插值插值插值旋转式L功能联系起来。
In this note we propose a new construction of cyclotomic p-adic L-functions attached to classical modular cuspidal eigenforms. This allows us to cover most known cases to date and provides a method which is amenable to generalizations to automorphic forms on arbitrary groups. In the classical setting of GL2 over Q this allows us to construct the p-adic L-function in the so far uncovered extremal case which arises under the unlikely hypothesis that p-th Hecke polynomial has a double root. Although Tate's conjecture implies that this case should never take place for GL2/Q, the obvious generalization does exist in nature for Hilbert cusp forms over totally real number fields of even degree and this article proposes a method which should adapt to this setting. We further study the admissibility and the interpolation properties of these extremal p-adic L-functions, and relate them to the two-variable p-adic L-function interpolating cyclotomic p-adic L-functions along a Coleman family.
