{"title":"Infinite Paley graphs","authors":"G. Jones","doi":"10.26493/2590-9770.1365.884","DOIUrl":null,"url":null,"abstract":"Infinite analogues of the Paley graphs are constructed, based on uncountably many infinite but locally finite fields. Weil's estimate for character sums shows that they are all isomorphic to the random or universal graph of Erd\\H os, Renyi and Rado. Automorphism groups and connections with model theory are considered.","PeriodicalId":36246,"journal":{"name":"Art of Discrete and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Art of Discrete and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26493/2590-9770.1365.884","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
Infinite analogues of the Paley graphs are constructed, based on uncountably many infinite but locally finite fields. Weil's estimate for character sums shows that they are all isomorphic to the random or universal graph of Erd\H os, Renyi and Rado. Automorphism groups and connections with model theory are considered.
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