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.