{"title":"在Golay-Shapiro-Like Sequence上","authors":"J. Allouche","doi":"10.1515/udt-2016-0021","DOIUrl":null,"url":null,"abstract":"Abstract A recent paper by P. Lafrance, N. Rampersad, and R. Yee studies the sequence of occurrences of 10 as a scattered subsequence in the binary expansion of integers. They prove in particular that the summatory function of this sequence has the “root N” property, analogously to the summatory function of the Golay-Shapiro sequence. We prove here that the root N property does not hold if we twist the sequence by powers of a complex number of modulus one, hence showing a fundamental difference with the Golay-Shapiro sequence.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"15 1","pages":"205 - 210"},"PeriodicalIF":0.0000,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"On a Golay-Shapiro-Like Sequence\",\"authors\":\"J. Allouche\",\"doi\":\"10.1515/udt-2016-0021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract A recent paper by P. Lafrance, N. Rampersad, and R. Yee studies the sequence of occurrences of 10 as a scattered subsequence in the binary expansion of integers. They prove in particular that the summatory function of this sequence has the “root N” property, analogously to the summatory function of the Golay-Shapiro sequence. We prove here that the root N property does not hold if we twist the sequence by powers of a complex number of modulus one, hence showing a fundamental difference with the Golay-Shapiro sequence.\",\"PeriodicalId\":23390,\"journal\":{\"name\":\"Uniform distribution theory\",\"volume\":\"15 1\",\"pages\":\"205 - 210\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Uniform distribution theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/udt-2016-0021\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uniform distribution theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/udt-2016-0021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
摘要
P. Lafrance, N. Rampersad和R. Yee最近的一篇论文研究了整数二进制展开中10作为分散子序列的出现序列。他们特别证明了这个序列的求和函数具有“根N”性质，类似于Golay-Shapiro序列的求和函数。我们在这里证明了如果我们以模为1的复数的幂来扭转序列，则根N的性质不成立，从而显示了与Golay-Shapiro序列的根本区别。
Abstract A recent paper by P. Lafrance, N. Rampersad, and R. Yee studies the sequence of occurrences of 10 as a scattered subsequence in the binary expansion of integers. They prove in particular that the summatory function of this sequence has the “root N” property, analogously to the summatory function of the Golay-Shapiro sequence. We prove here that the root N property does not hold if we twist the sequence by powers of a complex number of modulus one, hence showing a fundamental difference with the Golay-Shapiro sequence.
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