Variation of p-adic Newton polygons for L-functions of exponential sums
Variation of p-adic Newton polygons for L-functions of exponential sums
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DOI：
10.4310/ajm.2004.v8.n3.a4
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发表时间：
2004-09
影响因子：
0.6
通讯作者：
D. Wan
中科院分区：
文献类型：
--
作者：
D. Wan
在本文中，我们继续发展通用牛顿多边形的系统分解理论（18），该牛顿多边形附加到有限域上的一系列 zeta 函数，更一般地说是有限域上 n 维指数和的 L 函数族。我们的目标是为通用牛顿多边形建立一个新的塌缩分解定理（定理 3.7）。给出了 zeta 函数和 L 函数的许多应用，包括 Adolphson-Sperber 猜想 (2) 的其余 3 维和 4 维情况的完整形式，这些在 (18) 中尚未解决。为了使本文更具可读性和实用性，我们提供了扩展的介绍性部分以及详细的示例来说明如何使用主要定理。
In this paper, we continue to develop the systematic decomposition theory (18) for the generic Newton polygon attached to a family of zeta functions over finite fields and more generally a family of L-functions of n-dimensional exponential sums over finite fields. Our aim is to establish a new collapsing decomposition theorem (Theorem 3.7) for the generic Newton polygon. A number of applications to zeta functions and L-functions are given, including the full form of the remaining 3 and 4-dimensional cases of the Adolphson-Sperber conjecture (2), which were left un-resolved in (18). To make the paper more readable and useful, we have included an expanded introductory section as well as detailed examples to illustrate how to use the main theorems.