{"title":"具有可约多项式的指数和","authors":"C. Dartyge, G. Martin","doi":"10.19086/da.10793","DOIUrl":null,"url":null,"abstract":"Hooley proved that if $f\\in \\Bbb Z [X]$ is irreducible of degree $\\ge 2$, then the fractions $\\{ r/n\\}$, $0<r<n$ with $f(r)\\equiv 0\\pmod n$, are uniformly distributed in $(0,1)$. In this paper we study such problems for reducible polynomials of degree $\\le 3$. In particular, we establish asymptotic formulas for exponential sums over these normalized roots.","PeriodicalId":37312,"journal":{"name":"Discrete Analysis","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2018-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Exponential sums with reducible polynomials\",\"authors\":\"C. Dartyge, G. Martin\",\"doi\":\"10.19086/da.10793\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Hooley proved that if $f\\\\in \\\\Bbb Z [X]$ is irreducible of degree $\\\\ge 2$, then the fractions $\\\\{ r/n\\\\}$, $0<r<n$ with $f(r)\\\\equiv 0\\\\pmod n$, are uniformly distributed in $(0,1)$. In this paper we study such problems for reducible polynomials of degree $\\\\le 3$. In particular, we establish asymptotic formulas for exponential sums over these normalized roots.\",\"PeriodicalId\":37312,\"journal\":{\"name\":\"Discrete Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2018-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.19086/da.10793\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.19086/da.10793","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
期刊介绍：
Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.
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