Estimates for exponential sums with a large automorphism group
Author | Rojas León, Antonio |
Department | Universidad de Sevilla. Departamento de álgebra |
Date | 2012 |
Published in | Contemporary Mathematics, 566, 43-61. |
Document type | Article |
Abstract | 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 = Fq for two classes of polynomials which are invariant ... 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 = Fq for two classes of polynomials which are invariant under a large abelian group of automorphisms of the affine line A1 k: those invariant under translation by elements of k and those invariant under homotheties with ratios in a large subgroup of the multiplicative group of k. In both cases, we are able to improve the bound by a factor of √q over an extension.f k of cardinality sufficiently large compared to the degree of f. |
Cite | Rojas León, A. (2012). Estimates for exponential sums with a large automorphism group. Contemporary Mathematics, 566, 43-61. |
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DOI:
10.1090/conm/566/11214
Editor´s version:
http://dx.doi.org/10.1090/conm/566/11214