Variation of p-adic Newton polygons for L-functions of exponential sums

Abstract

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 unresolved 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.