On the Values of Kloosterman Sums

被引：6
|
作者：
Shparlinski, Igor E. [1 ]
机构：
[1] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2009年 / 55卷 / 06期
关键词：
Bent functions; Kloosterman sums; Lucas and Lehmer numbers; ELLIPTIC-CURVES; IRREDUCIBLE POLYNOMIALS; PRIMITIVE DIVISORS; INTEGERS;
D O I：
10.1109/TIT.2009.2018320
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Given a prime p and a positive integer n, we show that the shifted Kloosterman sums Sigma (x is an element of Fpn) psi (x + ax(pn-2)) = Sigma (x is an element of F+pn) psi(x + ax(-1)) + 1, a is an element of F(pn)* where psi is a nontrivial additive character of a finite field F(pn) of p(n) elements, do not vanish if a belongs to a small sublield F(pm) subset of F(pn). This complements recent results of P. Charpin and G. Gong which in turn were motivated by some applications to bent functions.
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页码：2599 / 2601
页数：3
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