论文标题
在诺斯科特（Northcott）的特殊值中
On the Northcott property for special values of L-functions
论文作者
论文摘要
我们建议对诺斯科特，博戈莫洛夫和莱默特性进行调查，以进行特殊的L功能值。我们首先为这三个属性引入了公理方法。然后，我们将重点放在诺斯科特（Northcott）的财产上，以获得特殊的L功能值。对于纯动机的L功能，我们证明了位于临界条左侧的特殊值的诺斯科特属性，假设所涉及的L功能满足了一些预期的特性。在关键条带上，重点关注数字字段的Dedekind Zeta函数，我们证明，这种属性不能以一个特殊的值来达到特殊值，而是特殊值以零为零，在这种情况下，我们给出了相关的定量估计。
We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of L-functions. We first introduce an axiomatic approach to these three properties. We then focus on the Northcott property for special values of L-functions. In the case of L-functions of pure motives, we prove a Northcott property for special values located at the left of the critical strip, assuming that the L-functions in question satisfy some expected properties. Inside the critical strip, focusing on the Dedekind zeta function of number fields, we prove that such a property does not hold for the special value at one, but holds for the special value at zero, and we give a related quantitative estimate in this case.
