Abstract
In this paper, we study the Newton polygon of the [Formula: see text]-function of a generalized Kloosterman polynomial with two variables over finite fields. We give the explicit form of the monomial basis of the top dimensional cohomology space of the [Formula: see text]-adic complex associated to the [Formula: see text]-function. One consequence of this result is a concrete method for computing the Hodge polygon. Using decomposition theorems of Wan, we determine when a generalized Kloosterman polynomial is ordinary and when its Newton polytope is generically ordinary.
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