T-adic Exponential Sums over Finite Fields
نویسندگان
چکیده
T -adic exponential sums associated to a Laurent polynomial f are introduced. They interpolate all classical p-power order exponential sums associated to f . The Hodge bound for the Newton polygon of L-functions of T -adic exponential sums is established. This bound enables us to determine, for all m, the Newton polygons of Lfunctions of p-power order exponential sums associated to an f which is ordinary for m = 1. Deeper properties of L-functions of T -adic exponential sums are also studied. Along the way, new open problems about the T -adic exponential sum itself are discussed.
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