{"title":"三元环多项式的平坦性","authors":"Bin Zhang","doi":"10.4171/rsmup/47","DOIUrl":null,"url":null,"abstract":"It is well known that all of the prime cyclotomic polynomials and binary cyclotomic polynomials are flat, and the flatness of ternary cyclotomic polynomials is much more complicated. Let p < q < r be odd primes such that zr ≡ ±1 (mod pq), where z is a positive integer. So far, the classification of flat ternary cyclotomic polynomials for 1 ≤ z ≤ 5 has been given. In this paper, for z = 6 and q ≡ ±1 (mod p), we give the necessary and sufficient conditions for ternary cyclotomic polynomials Φpqr(x) to be flat. Mathematics Subject Classification (2010). 11B83, 11C08, 11N56.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"463 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The flatness of ternary cyclotomic polynomials\",\"authors\":\"Bin Zhang\",\"doi\":\"10.4171/rsmup/47\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is well known that all of the prime cyclotomic polynomials and binary cyclotomic polynomials are flat, and the flatness of ternary cyclotomic polynomials is much more complicated. Let p < q < r be odd primes such that zr ≡ ±1 (mod pq), where z is a positive integer. So far, the classification of flat ternary cyclotomic polynomials for 1 ≤ z ≤ 5 has been given. In this paper, for z = 6 and q ≡ ±1 (mod p), we give the necessary and sufficient conditions for ternary cyclotomic polynomials Φpqr(x) to be flat. Mathematics Subject Classification (2010). 11B83, 11C08, 11N56.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"463 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/rsmup/47\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/47","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is well known that all of the prime cyclotomic polynomials and binary cyclotomic polynomials are flat, and the flatness of ternary cyclotomic polynomials is much more complicated. Let p < q < r be odd primes such that zr ≡ ±1 (mod pq), where z is a positive integer. So far, the classification of flat ternary cyclotomic polynomials for 1 ≤ z ≤ 5 has been given. In this paper, for z = 6 and q ≡ ±1 (mod p), we give the necessary and sufficient conditions for ternary cyclotomic polynomials Φpqr(x) to be flat. Mathematics Subject Classification (2010). 11B83, 11C08, 11N56.
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