{"title":"交替多重t值:加权和、对偶性和维数猜想","authors":"Ce Xu, Jianqiang Zhao","doi":"10.1007/s11139-023-00782-6","DOIUrl":null,"url":null,"abstract":"In this paper, we define some weighted sums of the alternating multiple T-values (AMTVs) and study several duality formulas for them. Then we introduce the alternating version of the convoluted T-values and Kaneko–Tsumura $$\\psi $$ -function, which are proved to be closely related to the AMTVs. At the end of the paper, we study the $$\\mathbb {Q}$$ -vector space generated by the AMTVs of any fixed weight w and provide some evidence for the conjecture that their dimensions $$\\{d_w\\}_{w\\ge 1}$$ form the tribonacci sequence 1, 2, 4, 7, 13, ....","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Alternating multiple T-values: weighted sums, duality, and dimension conjecture\",\"authors\":\"Ce Xu, Jianqiang Zhao\",\"doi\":\"10.1007/s11139-023-00782-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we define some weighted sums of the alternating multiple T-values (AMTVs) and study several duality formulas for them. Then we introduce the alternating version of the convoluted T-values and Kaneko–Tsumura $$\\\\psi $$ -function, which are proved to be closely related to the AMTVs. At the end of the paper, we study the $$\\\\mathbb {Q}$$ -vector space generated by the AMTVs of any fixed weight w and provide some evidence for the conjecture that their dimensions $$\\\\{d_w\\\\}_{w\\\\ge 1}$$ form the tribonacci sequence 1, 2, 4, 7, 13, ....\",\"PeriodicalId\":54511,\"journal\":{\"name\":\"Ramanujan Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ramanujan Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11139-023-00782-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-023-00782-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Alternating multiple T-values: weighted sums, duality, and dimension conjecture
In this paper, we define some weighted sums of the alternating multiple T-values (AMTVs) and study several duality formulas for them. Then we introduce the alternating version of the convoluted T-values and Kaneko–Tsumura $$\psi $$ -function, which are proved to be closely related to the AMTVs. At the end of the paper, we study the $$\mathbb {Q}$$ -vector space generated by the AMTVs of any fixed weight w and provide some evidence for the conjecture that their dimensions $$\{d_w\}_{w\ge 1}$$ form the tribonacci sequence 1, 2, 4, 7, 13, ....
期刊介绍:
The Ramanujan Journal publishes original papers of the highest quality in all areas of mathematics influenced by Srinivasa Ramanujan. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections.
The following prioritized listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interest:
Hyper-geometric and basic hyper-geometric series (q-series) * Partitions, compositions and combinatory analysis * Circle method and asymptotic formulae * Mock theta functions * Elliptic and theta functions * Modular forms and automorphic functions * Special functions and definite integrals * Continued fractions * Diophantine analysis including irrationality and transcendence * Number theory * Fourier analysis with applications to number theory * Connections between Lie algebras and q-series.