Cyclotomy of Weil sums of binomials

JOURNAL OF NUMBER THEORY

卷:154

Article

Aubry, Yves^1,2  Katz, Daniel J.³  Langevin, Philippe¹ 

[1] Univ Toulon & Var, Inst Math Toulon, F-83957 La Garde, France

[2] Aix Marseille Univ, CNRS, UMR 7373, Inst Math Marseille, F-13288 Marseille 9, France

[3] Calif State Univ Northridge, Dept Math, Northridge, CA 91330 USA

关键词: Weil sum;    Character sum;    Finite field;    Cyclotomy;   

DOI  :  10.1016/j.jnt.2015.02.011

来源: Elsevier

【 摘 要 】

The Well sum W-K,W-d (a) = Sigma(x is an element of) psi (xd + ax )where K is a finite field, psi is an additive character of K, d is coprime to vertical bar K (X)vertical bar, and a is an element of K-X arises often in number-theoretic calculations, and in applications to finite geometry, cryptography, digital sequence design, and coding theory. Researchers are especially interested in the case where W-K,W-d (a) assumes three distinct values as a runs through K-X. A Galois-theoretic approach, combined with p-divisibility results on Gauss sums, is used here to prove a variety of new results that constrain which fields K and exponents d support three-valued Weil sums, and restrict the values that such Weil sums may assume. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free