Estimates for exponential sums with a large automorphism group
Antonio Rojas‐León · Contemporary mathematics - American Mathematical Society · 2012
We prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated to a polynomial over a finite field k = F q k=\mathbb F_q for two classes of polynomials which are invariant under a large abelian group of automorphisms of the affine line A k 1 \mathbb A^1_k : those invariant under translation by elements of k k and those invariant under homotheties with ratios in a large subgroup of the multiplicative group of k k . In both cases, we are able to improve the bound by a factor of q \sqrt {q} over an extension of k k of cardinality sufficiently large compared to the degree of f f .