{"title":"多项式集合中的算术","authors":"M. Hbaib, Y. Laabidi","doi":"10.12816/0006179","DOIUrl":null,"url":null,"abstract":"Let be a formal series with deg( ) 2, the aim of this paper is to prove that the maximal length of the nite -fractional parts in the -expansion of product of two beta-polynomials (a formal series that have not -fractional part), denoted L ( ) is nite when is Pisot or Salem series. Especially, we give its exact value if have one conjugate with absolute value smaller than 1 j j and if is a Pisot series verifying d +Ad 1 d 1 + +A0 = 0 such that deg( ) = m 2 and deg(A0) = s deg(Ai) 80 i d 2.","PeriodicalId":210748,"journal":{"name":"International Journal of Open Problems in Computer Science and Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Arithmetics in the set of beta-polynomials\",\"authors\":\"M. Hbaib, Y. Laabidi\",\"doi\":\"10.12816/0006179\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let be a formal series with deg( ) 2, the aim of this paper is to prove that the maximal length of the nite -fractional parts in the -expansion of product of two beta-polynomials (a formal series that have not -fractional part), denoted L ( ) is nite when is Pisot or Salem series. Especially, we give its exact value if have one conjugate with absolute value smaller than 1 j j and if is a Pisot series verifying d +Ad 1 d 1 + +A0 = 0 such that deg( ) = m 2 and deg(A0) = s deg(Ai) 80 i d 2.\",\"PeriodicalId\":210748,\"journal\":{\"name\":\"International Journal of Open Problems in Computer Science and Mathematics\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Open Problems in Computer Science and Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12816/0006179\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Open Problems in Computer Science and Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12816/0006179","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let be a formal series with deg( ) 2, the aim of this paper is to prove that the maximal length of the nite -fractional parts in the -expansion of product of two beta-polynomials (a formal series that have not -fractional part), denoted L ( ) is nite when is Pisot or Salem series. Especially, we give its exact value if have one conjugate with absolute value smaller than 1 j j and if is a Pisot series verifying d +Ad 1 d 1 + +A0 = 0 such that deg( ) = m 2 and deg(A0) = s deg(Ai) 80 i d 2.
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