{"title":"具有加法性质的Ax定理","authors":"E. Hrushovski","doi":"10.4171/emss/47","DOIUrl":null,"url":null,"abstract":"Motivated by Emmanuel Kowalski's exponential sums over definable sets in finite fields, we generalize theorems of Ax and Chatzidakis-Van den Dries-Macintyre to pseudo-finite fields with an additive character, in a continuous logic setting.","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2019-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Ax’s theorem with an additive character\",\"authors\":\"E. Hrushovski\",\"doi\":\"10.4171/emss/47\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by Emmanuel Kowalski's exponential sums over definable sets in finite fields, we generalize theorems of Ax and Chatzidakis-Van den Dries-Macintyre to pseudo-finite fields with an additive character, in a continuous logic setting.\",\"PeriodicalId\":43833,\"journal\":{\"name\":\"EMS Surveys in Mathematical Sciences\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2019-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EMS Surveys in Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/emss/47\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EMS Surveys in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/emss/47","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
摘要
受Emmanuel Kowalski在有限域中可定义集上的指数和的启发，我们在连续逻辑环境中将Ax和Chatzidakis Van den Dries Macintyre的定理推广到具有加性的伪有限域。
Motivated by Emmanuel Kowalski's exponential sums over definable sets in finite fields, we generalize theorems of Ax and Chatzidakis-Van den Dries-Macintyre to pseudo-finite fields with an additive character, in a continuous logic setting.
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