Character sums over norm groups
The author of this paper gives estimates of character sums of Weil type. These estimates are associated with polynomials and rational functions with coefficients in a quadratic extension \(k_{2}\) of a finite field \(k\) of \(q\) elements, additive and multiplicative characters of \(k_{2}\), and summed over the kernel of the norm map from \(k_{2}^{\times}\) to \(k^\times\). The bounds are of the magnitude \(O(\sqrt{q})\) with the implied constant depending on the degree of the polynomial and the total degree of the support of the rational function, similar to Weil's estimate over \(k\).
scientific article; zbMATH DE number 5004382