Speaker：Wei Cao（Minnan Normal University）

Time：2022-06-16, 10:30

Location：Tencent Meeting ID：144-310-955（No Password）

Abstract:

Let f be a non-degenerate Laurent polynomial over a finite field and L(f,T) the associated L-function of the toric exponential sums of f. The Newton polygon can be used to study the p-adic valuations of roots or poles of L(f,T), which has a lower bound called the Hodge polygon that depends only on the Newton polytope of f. These two polygons coincide when the coefficients of f are not zeros of the certain Hasse polynomial. Using the Dwork trace formula, we find a formula for the Hasse polynomial of the slope one side for a class of Laurent polynomials, which greatly generalizes the known results.