{"title":"函数场中的互易定律","authors":"Yoshinori Hamahata","doi":"10.1007/s00013-024-02006-9","DOIUrl":null,"url":null,"abstract":"<div><p>We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"123 1","pages":"49 - 56"},"PeriodicalIF":0.5000,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A reciprocity law in function fields\",\"authors\":\"Yoshinori Hamahata\",\"doi\":\"10.1007/s00013-024-02006-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.</p></div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":\"123 1\",\"pages\":\"49 - 56\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-02006-9\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-02006-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We generalize Gauss’ lemma over function fields, and establish a reciprocity law for power residue symbols. As an application, a reciprocity law for power residue symbols is established in totally imaginary function fields.
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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