Asian Journal of Mathematics
Volume 8 (2004)
Variation of p-adic Newton polygons for L-functions of exponential sums
Pages: 427 – 472
In this paper, we continue to develop the systematic decomposition theory  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 , which were left unresolved in . 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.