{"title":"A Recursive Formula and an Estimation for a Specific Exponential Sum","authors":"Xiwang Cao null, Liqin Qian","doi":"10.4208/cmr.2021-0030","DOIUrl":null,"url":null,"abstract":"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","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究通讯","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/cmr.2021-0030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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