Expressions of Schur multiple zeta-functions of anti-hook type by zeta-functions of root systems

Matsumoto, Kohji; Nakasuji, Maki

doi:10.5486/pmd.2021.8869

Cited by 3 publications

(2 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now we are ready to prove the main results in the present paper. Our aim is to generalize the results in Section 3 to more general content-parametrized Schur multiple zeta-functions ζ λ (s s s) which can be written in terms of {z k } with content k. The results which we will prove in this section are Theorem 4.1 and Theorem 4.2, which are analogues of [MN,Theorem 3.2] and of [MN,Theorem 4.1], respectively. First, as a generalization of Theorem 3.1, we prove the following theorem.…”

Section: Expressions Of Content-parametrized Schur Multiple Zeta-func...mentioning

confidence: 90%

Expressions of content-parametrized Schur multiple zeta-functions via the Giambelli formula

Matsumoto¹,

Nakasuji²

2023

Preprint

View full text Add to dashboard Cite

In this article, we consider the expressions for content-parametrized Schur multiple zeta-functions in terms of multiple zeta-functions of Euler-Zagier type and their star-variants, or in terms of modified zeta-functions of root systems. First of all, we focus on the Schur multiple zeta-function of hook type. And then, applying the Giambelli formula and induction argument, we obtain the expressions for general contentparametrized Schur multiple zeta-functions.

show abstract

Section: Expressions Of Content-parametrized Schur Multiple Zeta-func...mentioning

confidence: 90%

Expressions of content-parametrized Schur multiple zeta-functions via the Giambelli formula

Matsumoto¹,

Nakasuji²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Due to their surprising and sometimes mysterious appearance in the study of many branches of mathematics and theoretical physics, these special values have attracted a lot of attention and interest in the past three decades (for example, see the book by the second author [18]). A common generalization of the MZVs and MZSVs is given by the Schur multiple zeta values [10,11], which are defined using the skew Young tableaux. For example, for integers a, b, d, e, f ≥ 1, c, g ≥ 2, the following sum is an example of Schur multiple zeta values:…”

Section: Multiple Zeta Values (Mzvs) and Schur Mzvsmentioning

confidence: 99%

Explicit Relations Between Kaneko-Yamamoto Type Multiple Zeta Values and Related Variants

Xu¹,

Zhao²

2022

Kyushu J. Math.

View full text Add to dashboard Cite

In this paper we first establish several integral identities involving the multiple polylogarithm functions and the Kaneko-Tsumura A-function, which can be thought as a single-variable multiple polylogarithm function of level two. We find that these integrals can be expressed in terms of multiple zeta (star) values, their related variants (multiple tvalues, multiple T -values, multiple S-values, etc.), and multiple harmonic (star) sums and their related variants (multiple T -harmonic sums, multiple S-harmonic sums, etc.), which are closely related to some special types of Schur multiple zeta values and their generalizations. Using these integral identities, we prove many explicit evaluations of Kaneko-Yamamoto multiple zeta values and their related variants. Further, we derive some relations involving multiple zeta (star) values and their related variants.

show abstract

Cyclic relation for multiple zeta functions

Murahara

Onozuka

2022

Res. number theory

View full text Add to dashboard Cite

Expressions of Schur multiple zeta-functions of anti-hook type by zeta-functions of root systems

Cited by 3 publications

References 15 publications

Expressions of content-parametrized Schur multiple zeta-functions via the Giambelli formula

Expressions of content-parametrized Schur multiple zeta-functions via the Giambelli formula

Explicit Relations Between Kaneko-Yamamoto Type Multiple Zeta Values and Related Variants

Cyclic relation for multiple zeta functions

Contact Info

Product

Resources

About