{"title":"一类特定指数和的递归公式及估计","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":"{\"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}","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}
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