论文标题
野生kloosterman的大小在数字字段和功能字段中总和
The size of wild Kloosterman sums in number fields and function fields
论文作者
论文摘要
我们研究了P-Adic Hyper-Koolosterman总和，这是Kloosterman总和的概括，该参数k在k = 2时恢复了经典的kloosterman总和，在一般的p-adic环上，甚至相等的特征局部环。当k不被P排除时，可以通过简单的固定相估计来评估这些，从而使它们的大小基本上锐利。我们给出了更复杂的固定相估计，以在k排除p的情况下对其进行评估。这给出了上限和下限显示上限本质上是锋利的。在$ \ mathbb z_p $的情况下，这概括了Cochrane，Liu和Zhen的先前已知界限。相等特征的情况下的下限有两个用于功能场数理论的应用，表明某些短间隔总和和某些dirichlet l功能的时刻并不希望取消平方根。
We study p-adic hyper-Kloosterman sums, a generalization of the Kloosterman sum with a parameter k that recovers the classical Kloosterman sum when k=2, over general p-adic rings and even equal characteristic local rings. These can be evaluated by a simple stationary phase estimate when k is not divisible by p, giving an essentially sharp bound for their size. We give a more complicated stationary phase estimate to evaluate them in the case when k is divisible by p. This gives both an upper bound and a lower bound showing the upper bound is essentially sharp. This generalizes previously known bounds of Cochrane, Liu, and Zhen in the case of $\mathbb Z_p$. The lower bounds in the equal characteristic case have two applications to function field number theory, showing that certain short interval sums and certain moments of Dirichlet L-functions do not, as one might hope, admit square-root cancellation.
