四次塞勒姆数是非倒数2-皮索数的马勒测度

IF 0.3 4区数学 Q4 MATHEMATICS

Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-01-08 DOI:10.5802/JTNB.1145

Toufik Zaïmi

{"title":"四次塞勒姆数是非倒数2-皮索数的马勒测度","authors":"Toufik Zaïmi","doi":"10.5802/JTNB.1145","DOIUrl":null,"url":null,"abstract":"Motivated by a question of M. J. Bertin, we obtain parametrizations of minimal polynomials of quartic Salem numbers, say α, which are Mahler measures of non-reciprocal 2-Pisot numbers. This allows us to determine all such numbers α with a given trace, and to deduce that for any natural number t (resp. t ≥ 2) there is a quartic Salem number of trace t which is (resp. which is not) a Mahler measure of a non-reciprocal 2-Pisot number.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":"26 1","pages":"877-889"},"PeriodicalIF":0.3000,"publicationDate":"2021-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers\",\"authors\":\"Toufik Zaïmi\",\"doi\":\"10.5802/JTNB.1145\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by a question of M. J. Bertin, we obtain parametrizations of minimal polynomials of quartic Salem numbers, say α, which are Mahler measures of non-reciprocal 2-Pisot numbers. This allows us to determine all such numbers α with a given trace, and to deduce that for any natural number t (resp. t ≥ 2) there is a quartic Salem number of trace t which is (resp. which is not) a Mahler measure of a non-reciprocal 2-Pisot number.\",\"PeriodicalId\":48896,\"journal\":{\"name\":\"Journal De Theorie Des Nombres De Bordeaux\",\"volume\":\"26 1\",\"pages\":\"877-889\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-01-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal De Theorie Des Nombres De Bordeaux\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/JTNB.1145\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal De Theorie Des Nombres De Bordeaux","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/JTNB.1145","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

在M. J. Bertin问题的激励下，我们得到了四次Salem数的最小多项式的参数化，如α，它是非互反2-Pisot数的Mahler测度。这允许我们用给定的迹来确定所有这样的数α，并推导出对于任何自然数t (p。t≥2时，轨迹t有一个四次塞勒姆数，即(p。它不是非倒数2-皮索数的马勒测度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Quartic Salem numbers which are Mahler measures of non-reciprocal 2-Pisot numbers

Motivated by a question of M. J. Bertin, we obtain parametrizations of minimal polynomials of quartic Salem numbers, say α, which are Mahler measures of non-reciprocal 2-Pisot numbers. This allows us to determine all such numbers α with a given trace, and to deduce that for any natural number t (resp. t ≥ 2) there is a quartic Salem number of trace t which is (resp. which is not) a Mahler measure of a non-reciprocal 2-Pisot number.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal De Theorie Des Nombres De Bordeaux MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The Journal de Théorie des Nombres de Bordeaux publishes original papers on number theory and related topics (not published elsewhere).