一类特定指数和的递归公式及估计

数学研究通讯 Pub Date : 2022-01-01 DOI:10.4208/cmr.2021-0030

Xiwang Cao null, Liqin Qian

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引用次数: 0

摘要

设Fq是一个有限域，Fq是Fq的一个扩展。设f (x)∈Fq[x]是一个n次多项式，且gcd(n,q) = 1。给出了指数和∑c∈Fqs χ (s)(f (x))的递推公式。设a和b是Fq中的两个元素，其中a为6= 0,u为正整数。我们得到了指数和∑c∈F∗qs χ(s)(acu+bc−1)的估计，其中χ(s)是Fq的加性特征χ的提升。并给出了由这些指数和构造的数列的一些性质。AMS学科分类:11T23

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A Recursive Formula and an Estimation for a Specific Exponential Sum

Let Fq be a finite field and Fqs be an extension of Fq. Let f (x) ∈ Fq[x] be a polynomial of degree n with gcd(n,q) = 1. We present a recursive formula for evaluating the exponential sum ∑c∈Fqs χ (s)( f (x)). Let a and b be two elements in Fq with a 6= 0, u be a positive integer. We obtain an estimate for the exponential sum ∑c∈F∗ qs χ(s)(acu+bc−1), where χ(s) is the lifting of an additive character χ of Fq. Some properties of the sequences constructed from these exponential sums are provided too. AMS subject classifications: 11T23

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数学研究通讯

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