T-ADIC L-FUNCTIONS OF p-ADIC EXPONENTIAL SUMS
نویسندگان
چکیده
The T -adic deformation of p-adic exponential sums is defined. It interpolates all classical p-power order exponential sums over a finite field. Its generating L-function is a T -adic entire function. We give a lower bound for its T -adic Newton polygon and show that the lower bound is often sharp. We also study the variation of this L-function in an algebraic family, in particular, the T -adic version of the AdolphsonSperber conjecture on generic ordinariness, Wan’s limiting conjecture on generic Newton polygon, and Dwork’s unit root conjecture. These raise a number of new questions.
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