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This paper introduces a set of finite summation formulas and utilize them to establish various functional relationships involving the multivariable Hurwitz-Lerch zeta function. Additionally, the paper examines several examples of these…

Number Theory · Mathematics 2023-06-23 Robert Reynolds

In the study on multiple zeta values, the duality formula is one of the families of basic relations and plays an important role in the investigation of algebraic structure of the space spanned by all multiple zeta values along with the…

Number Theory · Mathematics 2021-09-30 Maki Nakasuji , Yasuo Ohno

This thesis is a study of algebraic and geometric relations between multizeta values. In chapter 2, we prove a result which gives the dimension of the associated depth-graded pieces of the double shuffle Lie algebra in depths 1 and 2. In…

Number Theory · Mathematics 2009-11-16 Sarah Carr

Using a polylogarithmic identity, we express the values of $\zeta$ at odd integers $2n+1$ as integrals over unit $n-$dimensional hypercubes of simple functions involving products of logarithms. We also prove a useful property of those…

Number Theory · Mathematics 2016-12-15 Thomas Sauvaget

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

Number Theory · Mathematics 2022-08-26 Maki Nakasuji , Wataru Takeda

Two classes of relations for multiple zeta values are handled algebraically. A restricted sum formula is proved by Eie, Liaw and Ong. The derivation relation is proved by Ihara, Kaneko and Zagier. In this paper we show the latter implies…

Number Theory · Mathematics 2013-03-05 Tatsushi Tanaka

We confirm a conjecture about the construction of basis elements for the multiple zeta values (MZVs) at weight 27 and weight 28. Both show as expected one element that is twofold extended. This is done with some lengthy computer algebra…

Mathematical Physics · Physics 2011-05-11 J. Kuipers , J. A. M. Vermaseren

The sum formula for finite and symmetric multiple zeta values, established by Wakabayashi and the authors, implies that if the weight and depth are fixed and the specified component is required to be more than one, then the values sum up to…

Number Theory · Mathematics 2019-12-25 Hideki Murahara , Shingo Saito

Nakasuji, Phuksuwan, and Yamasaki defined the Schur multiple zeta values and gave iterated integral expressions of the Schur multiple zeta values of the ribbon type. This paper generalizes their integral expressions to the ones of more…

Number Theory · Mathematics 2023-03-08 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

We define discrete nested sums over integer points for symbols on the real line, which obey stuffle relations whenever they converge. They relate to Chen integrals of symbols via the Euler-MacLaurin formula. Using a suitable holomorphic…

Number Theory · Mathematics 2009-12-11 Dominique Manchon , Sylvie Paycha

We know at least two ways to generalize multiple zeta(-star) values, or MZ(S)Vs for short, which are $q$-analogue and $t$-interpolation. The $q$-analogue of MZ(S)Vs, or $q$MZ(S)Vs for short, was introduced by Bradley, Okuda and Takeyama,…

Number Theory · Mathematics 2016-09-06 Noriko Wakabayashi

Multiple $T$-values, a variant of multiple zeta values of level two, were introduced and studied by Kaneko and Tsumura. This paper will introduce iterated log-tangent integrals and discuss their relations with multiple $T$-values. We will…

Number Theory · Mathematics 2023-01-18 Ryota Umezawa

We evaluate several classes of high weight hypergeometric series via Multiple Zeta Values.

Number Theory · Mathematics 2020-09-29 Ming Hao Zhao

This paper provides a systematic study of symmetry properties for cyclotomic multiple Hurwitz zeta values with multiple variables and parameters by applying the methods of contour integration and the residue theorem. The main contributions…

Number Theory · Mathematics 2026-02-12 Ce Xu

We study multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on multiple zeta values from relations in Rota--Baxter algebras.

Number Theory · Mathematics 2014-10-14 Kurusch Ebrahimi-Fard , Li Guo

We study a general type of series and relate special cases of it to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values of the Arakawa-Kaneko zeta function, complementing and generalizing earlier…

Number Theory · Mathematics 2018-07-03 Markus Kuba , Alois Panholzer

Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the iterated integral expressions of multiple zeta values become discretized. In this paper, we extend their result to the case of multiple polylogarithms and…

Number Theory · Mathematics 2024-04-24 Minoru Hirose , Toshiki Matsusaka , Shin-ichiro Seki

In this paper,we develop a novel representation of the zeta function expressed as the limiting difference between two structured double sums. This approach leads to a new and elegant identity involving maximum functions and additive terms,…

Number Theory · Mathematics 2025-11-03 Mahipal Gurram

The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.

Number Theory · Mathematics 2011-05-10 Zhong-hua Li

We prove a sum formula with 4 parameters among finite alternating multiple zeta values which can be regarded as an alternating version of the result of Kamano on finite multiple zeta values.

Number Theory · Mathematics 2022-02-22 Takumi Anzawa