Alternating multiple T-values: weighted sums, duality, and dimension conjecture

IF 0.6 3区数学 Q3 MATHEMATICS

Ramanujan Journal Pub Date : 2023-09-26 DOI:10.1007/s11139-023-00782-6

Ce Xu, Jianqiang Zhao

引用次数: 3

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, ....

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交替多重t值:加权和、对偶性和维数猜想

本文定义了交替多重t值(amtv)的一些加权和，并研究了它们的对偶公式。然后我们引入了交替版本的卷积t值和Kaneko-Tsumura $$\psi $$ -函数，证明了它们与amtv密切相关。在本文的最后，我们研究了任意定权w的amtv所产生的$$\mathbb {Q}$$ -向量空间，并为其维数$$\{d_w\}_{w\ge 1}$$构成tribonacci序列1,2,4,7,13，....的猜想提供了一些证据

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ramanujan Journal 数学-数学

CiteScore

1.40

自引率

14.30%

发文量

133

审稿时长

6-12 weeks

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.