A Stickleberger theorem for p-adic Gauss sums

الأصل · EN

We define "splitting functions of level l" for any integer l>0. These functions generalize Dwork's splitting functions: they allow us to represent additive characters of order pˡ. Then we use these functions to obtain a Stickleberger theorem on the p-adic valuation of new Gauss sums.