{"title":"有限域和椭圆曲线上的原始元","authors":"I. E. Shparlinskii","doi":"10.1070/SM1992V071N01ABEH001389","DOIUrl":null,"url":null,"abstract":"An asymptotic formula for the number of primitive polynomials of the form f (x) + a, a = 1, ..., h, where f (x)Fp[x], is obtained, \"on the average\" over all polynomials f of fixed degree, and an estimate for the number of \"sparse\" factorable polynomials is also obtained.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"27","resultStr":"{\"title\":\"ON PRIMITIVE ELEMENTS IN FINITE FIELDS AND ON ELLIPTIC CURVES\",\"authors\":\"I. E. Shparlinskii\",\"doi\":\"10.1070/SM1992V071N01ABEH001389\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An asymptotic formula for the number of primitive polynomials of the form f (x) + a, a = 1, ..., h, where f (x)Fp[x], is obtained, \\\"on the average\\\" over all polynomials f of fixed degree, and an estimate for the number of \\\"sparse\\\" factorable polynomials is also obtained.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"27\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V071N01ABEH001389\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V071N01ABEH001389","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 27
摘要
形式为f (x) + a, a = 1，…的原始多项式个数的渐近公式， h，其中得到f (x)Fp[x]，对所有固定次多项式f的“平均”，也得到了“稀疏”可因子多项式个数的估计。
ON PRIMITIVE ELEMENTS IN FINITE FIELDS AND ON ELLIPTIC CURVES
An asymptotic formula for the number of primitive polynomials of the form f (x) + a, a = 1, ..., h, where f (x)Fp[x], is obtained, "on the average" over all polynomials f of fixed degree, and an estimate for the number of "sparse" factorable polynomials is also obtained.
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