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In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,...,2. Our identities give analogues of Zagier's evaluation of \zeta(2,...,2,3,2,..., 2) and examples of a…

Number Theory · Mathematics 2014-06-06 Koji Tasaka , Shuji Yamamoto

The $t$-adic symmetric multiple zeta values were defined Jarossay, which have been studied as a real analogue of $\boldsymbol{p}$-adic finite multiple zeta values. In this paper, we consider the star analogues based on several…

Number Theory · Mathematics 2020-02-04 Minoru Hirose , Hideki Murahara , Masataka Ono

In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By…

Number Theory · Mathematics 2017-10-20 Ce Xu

We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of…

Number Theory · Mathematics 2018-07-04 Minoru Hirose , Hideki Murahara , Takuya Murakami

In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results of Hessami Pilehrood et al. As applications we prove several conjectures…

Number Theory · Mathematics 2018-04-06 Jianqiang Zhao

We present a new "integral=series" type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear…

Number Theory · Mathematics 2016-11-15 Masanobu Kaneko , Shuji Yamamoto

The cyclic sum formulas for multiple zeta and zeta-star values were respectively proved by Hoffman and Ohno, and Ohno and Wakabayashi. Kawasaki and Oyama obtained an analogous formulas for finite multiple zeta and zeta-star values. In this…

Number Theory · Mathematics 2020-09-30 Hideki Murahara

The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lison\v{e}k states that by inserting all cyclic permutations of some initial blocks of 2's into the multiple zeta value $ \zeta(1,3,\ldots,1,3) $ and summing, one obtains…

Number Theory · Mathematics 2017-04-28 Steven Charlton

Recently, the present authors jointly with Tauraso found a family of binomial identities for multiple harmonic sums (MHS) on strings $(\{2\}^a,c,\{2\}^b)$ that appeared to be useful for proving new congruences for MHS as well as new…

Number Theory · Mathematics 2018-06-26 Khodabakhsh Hessami Pilehrood , Tatiana Hessami Pilehrood

In 1998, Borwein, Bradley, Broadhurst and Lison\v{e}k posed two families of conjectural identities among multiple zeta values, later generalized by Charlton using his alternating block notation. In this paper, we prove a new class of…

Number Theory · Mathematics 2022-06-08 Minoru Hirose , Nobuo Sato

In this paper we present a new family of identities for multiple harmonic sums which generalize a recent result of Hessami Pilehrood et al. We then apply it to obtain a family of identities relating multiple zeta star values to alternating…

Number Theory · Mathematics 2019-02-20 Erin Linebarger , Jianqiang Zhao

In this paper we first establish several integral identities. These integrals are of the form \[\int_0^1 x^{an+b} f(x)\,dx\quad (a\in\{1,2\},\ b\in\{-1,-2\})\] where $f(x)$ is a single-variable multiple polylogarithm function or…

Number Theory · Mathematics 2023-11-07 Ce Xu , Jianqiang Zhao

Ohno-Wakabayashi's cyclic sum formula for multiple zeta-star values is generalized by Igarashi with one or two parameters. In this article, we give a possible answer for one of his problems about a generalization with three parameters.

Number Theory · Mathematics 2024-12-06 Hanamichi Kawamura , Anju Yokoi

In 2008, Muneta found explicit evaluation of the multiple zeta star value $\zeta^\star(\{3, 1\}^d)$, and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3-2-1 indices. In this paper, we provide another way of…

Number Theory · Mathematics 2018-06-28 Khodabakhsh Hessami Pilehrood , Tatiana Hessami Pilehrood

We define polynomials of one variable t whose values at t=0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the cyclic sum…

Number Theory · Mathematics 2012-03-07 Shuji Yamamoto

An identity involving symmetric sums of regularized multiple zeta-star values of harmonic type was proved by Hoffman. In this paper, we prove an identity of shuffle type. We use Bell polynomials appearing in the study of set partitions to…

Number Theory · Mathematics 2019-05-29 Tomoya Machide

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

Number Theory · Mathematics 2020-08-25 Hideki Murahara , Masataka Ono

In this paper, we establish some new identities of integrals involving multiple polylogarithm functions and their level two analogues in terms of Hurwitz-type multiple zeta (star) values. Using these identities, we provide new proofs of the…

Number Theory · Mathematics 2025-01-22 Masanobu Kaneko , Weiping Wang , Ce Xu , Jianqiang Zhao

We introduce an algebraic formulation of cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by…

Number Theory · Mathematics 2009-02-17 Tatsushi Tanaka , Noriko Wakabayashi

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
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