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Related papers: Ohno-type relation for interpolated multiple zeta …

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In this paper we give two idelic representations of the multiple zeta values - one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. Each of the representations leads to a…

Number Theory · Mathematics 2014-09-30 Ivan Horozov

Following Bachmann's recent work on bi-brackets and multiple Eisenstein series, Zudilin introduced the notion of multiple q-zeta brackets, which provides a q-analog of multiple zeta values possessing both shuffle as well as quasi-shuffle…

Number Theory · Mathematics 2016-08-16 Kurusch Ebrahimi-Fard , Dominique Manchon , Johannes Singer

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

We prove and conjecture several relations between multizeta values for $\mathbb{F}_q[t]$, focusing on zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular,…

Number Theory · Mathematics 2013-12-18 José Alejandro Lara Rodríguez , Dinesh S. Thakur

In this paper, we investigate three general forms of multiple zeta(-star) values. We use these values to give three new sum formulas for multiple zeta(-star) values with height $\leq 2$ and the evaluation of…

Number Theory · Mathematics 2022-02-09 Kwang-Wu Chen , Minking Eie

This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…

Number Theory · Mathematics 2023-09-18 Koji Tasaka

We define and study the interpolated finite multiple harmonic $q$-series. A generating function of the sums of the interpolated finite multiple harmonic $q$-series with fixed weight, depth and $i$-height is computed. Some Ohno-Zagier type…

Number Theory · Mathematics 2019-03-22 Zhonghua Li , Ende Pan

We study relations between the multizeta values for function fields introduced by D. Thakur. The product \zeta(a)\zeta(b) is a linear combination of multizeta values. For q=2, a full conjectural description of how the product of two zeta…

Number Theory · Mathematics 2011-08-25 José Alejandro Lara Rodríguez

We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta(3,2,\ldots,2)$ and multiple $t$-value $t\left(3,2,\ldots,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value…

Number Theory · Mathematics 2021-11-16 Sarth Chavan , Masato Kobayashi , Jorge Layja

In this paper, we obtain a general t-shuffle product formula, using which we derive a generalized Euler decomposition formula for interpolated multiple zeta values. We also provide the same formula in case of height one through two…

Number Theory · Mathematics 2026-02-03 Pitu Sarkar , Nita Tamang

It is known that there are infinitely many singularities of multiple zeta functions and the special values at non-positive integer points are indeterminate. In order to give a suitable rigorous meaning of the special values there, Furusho,…

Number Theory · Mathematics 2020-02-26 Nao Komiyama

We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…

Number Theory · Mathematics 2024-03-01 Takumi Maesaka , Shin-ichiro Seki , Taiki Watanabe

The sum formula for multiple zeta values are derived, via the Mellin transform, from the Euler connection formula and the Landen connection formula for polylogarithms. These connection formulas for multiple polylogarithms will be considered…

Number Theory · Mathematics 2007-05-23 Jun-ichi Okuda , Kimio Ueno

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

We present several formulas for some specific multiple $L$-values of conductor four. This grew out from the study of zeta functions of level four of Arakawa-Kaneko type. Closely related is a new version of multiple poly-Euler numbers and we…

Number Theory · Mathematics 2022-08-11 Masanobu Kaneko , Hirofumi Tsumura

In this paper we introduce and study double tails of multiple zeta values. We show, in particular, that they satisfy certain recurrence relations and deduce from this a generalization of Euler's classical formula…

Number Theory · Mathematics 2021-05-27 P. Akhilesh

Alternating variants of multiple poly-Bernoulli numbers and finite multiple zeta values in characteristic 0 and p This paper consists of two parts: the characteristic 0 part and the characteristic p part. In characteristic 0 part, we…

Number Theory · Mathematics 2021-04-16 Daichi Matsuzuki

This paper contains examples of shuffle relations among multiple Dedekind zeta values. Dedekind zeta values were defined by the author in his paper "Multiple Dedekind zeta functions". Here we concentrate on the cases of real or imaginary…

Number Theory · Mathematics 2018-11-21 Ivan Horozov

We introduce a new deformation of multiple zeta value (MZV). It has one parameter $\omega$ satisfying $0<\omega<2$ and recovers MZV in the limit as $\omega \to +0$. It is defined in the same algebraic framework as a $q$-analogue of multiple…

Number Theory · Mathematics 2024-07-01 Yoshihiro Takeyama

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