{"title":"Gaussian Primes in Narrow Sectors","authors":"Joshua Stucky","doi":"10.1093/qmath/haab009","DOIUrl":null,"url":null,"abstract":"We generalize a Theorem of Ricci and count Gaussian primes \n<tex>$\\mathfrak{p}$</tex>\n with short interval restrictions on both the norm and the argument of \n<tex>$\\mathfrak{p}$</tex>\n. We follow Heath-Brown's method for counting rational primes in short intervals.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":"72 4","pages":"1357-1377"},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://ieeexplore.ieee.org/document/9690910/","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We generalize a Theorem of Ricci and count Gaussian primes
$\mathfrak{p}$
with short interval restrictions on both the norm and the argument of
$\mathfrak{p}$
. We follow Heath-Brown's method for counting rational primes in short intervals.
期刊介绍：
The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.
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