论文标题
$ l $ - 符合广义的Kloosterman总和和$ P $ ADIC微分方程
$L$-functions for families of generalized Kloosterman sums and $p$-adic differential equations
论文作者
论文摘要
在本文中，我们专注于一个普遍的Kloosterman家族，总计在圆环上。通过对Haessig和Sperber的构造进行了一些更改，我们得出了一些相对的$ P $ -ADIC共同体，对应于$ L $ - 功能。我们提出了顶级共同学空间的明确形式的基础，因此要获得一种具体的方法来计算$ L $ functions的牛顿多边形的下限。使用GKZ系统的理论，我们为我们的家庭得出了DWork的变形方程。此外，在DWork的双重理论和变形理论的帮助下，建立了该方程的强大结构。我们的作品为DWork的猜想增加了一些新的证据。
In this paper, we focus on a family of generalized Kloosterman sums over the torus. With a few changes to Haessig and Sperber's construction, we derive some relative $p$-adic cohomologies corresponding to the $L$-functions. We present explicit forms of bases of top dimensional cohomology spaces, so to obtain a concrete method to compute lower bounds of Newton polygons of the $L$-functions. Using the theory of GKZ system, we derive the Dwork's deformation equation for our family. Furthermore, with the help of Dwork's dual theory and deformation theory, the strong Frobenius structure of this equation is established. Our work adds some new evidences for Dwork's conjecture.
