Gauss--Heilbronn Sums and Coverings of Deligne--Lusztig Type Curves

We study exponential sums on Witt vectors, known as Gauss–Heilbronn sums, and the curves whose Frobenius traces realize these sums via a Deligne–Lusztig type construction. For 3-typical Witt vectors of length two, we analyze Gauss–Heilbronn sums, from which we fully determine the Frobenius slopes of the associated curves.