MathematikaPub Date : 2023-10-26DOI: 10.1112/mtk.12227
Pranendu Darbar, Anirban Mukhopadhyay
{"title":"Correlation of multiplicative functions over \u0000 \u0000 \u0000 \u0000 F\u0000 q\u0000 \u0000 \u0000 [\u0000 x\u0000 ]\u0000 \u0000 \u0000 $mathbb {F}_q[x]$\u0000 : A pretentious approach","authors":"Pranendu Darbar, Anirban Mukhopadhyay","doi":"10.1112/mtk.12227","DOIUrl":"https://doi.org/10.1112/mtk.12227","url":null,"abstract":"<p>Let <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$mathcal {M}_n$</annotation>\u0000 </semantics></math> denote the set of monic polynomials of degree <i>n</i> over a finite field <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 <annotation>$mathbb {F}_q$</annotation>\u0000 </semantics></math> of <i>q</i> elements. For multiplicative functions <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>ψ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>ψ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$psi _1,psi _2$</annotation>\u0000 </semantics></math>, using the recently developed “pretentious method,” we establish a “local-global” principle for correlation functions of the form\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"70 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12227","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68181295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}