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Related papers: A unified approach to qMZVs

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This paper gives a new application of so-called connected sums, introduced recently by Seki and Yamamoto. Special about our approach is that it proves a duality for the Schlesinger-Zudilin and the Bradley-Zhao model of qMZVs simultaneously.…

Number Theory · Mathematics 2021-11-02 Benjamin Brindle

We introduce and study a ``level two'' analogue of finite multiple zeta values. We give conjectural bases of the space of finite Euler sums as well as that of usual finite multiple zeta values in terms of these newly defined elements. A…

Number Theory · Mathematics 2021-09-28 Masanobu Kaneko , Takuya Murakami , Amane Yoshihara

Multiple zeta values (MZVs) are real numbers which are defined by certain multiple series. Recently, many people have researched for relations among them and many relations are well known. In this paper, we get a new relation among them…

Number Theory · Mathematics 2015-12-29 Shin-ya Kadota

In [Ok] Okounkov studies a specific $q$-analogue of multiple zeta values and makes some conjectures on their algebraic structure. In this note we compare Okounkovs $q$-analogues to the generating function for multiple divisor sums defined…

Number Theory · Mathematics 2016-12-13 Henrik Bachmann , Ulf Kuehn

We define q-analogues of Mirzakhani's recursion for Weil-Petersson volumes and the Stanford-Witten recursion for super Weil-Petersson volumes. Okuyama recently introduced a q-deformation of the Gaussian Hermitian matrix model which produces…

Algebraic Geometry · Mathematics 2025-10-15 Norman Do , Paul Norbury

Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and…

Number Theory · Mathematics 2007-05-23 Taekyun Kim , SAeog-Hoon Rim

We use an injection method to prove a new class of partition inequalities involving certain $q$-products with two to four finitization parameters. Our new theorems are a substantial generalization of work by Andrews and of previous work by…

Combinatorics · Mathematics 2013-11-22 Alexander Berkovich , Keith Grizzell

We present several conjectures on multiple q-zeta values and on the role they play in certain problems of enumerative geometry.

Algebraic Geometry · Mathematics 2014-04-16 Andrei Okounkov

We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM} and developed the idea further in \cite{AS}. In this paper we study locally $M$-metrizable spaces and the products of $M$-metrizable spaces. Finally we…

General Topology · Mathematics 2017-07-04 Olli Hella

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 study a family of single variable integral representations for some products of $\zeta(2n+1)$, where $\zeta(z)$ is Riemann zeta function and $n$ is positive integer. Such representation involves the integral…

Number Theory · Mathematics 2021-01-12 Xiaowei Wang

We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class…

Number Theory · Mathematics 2014-05-27 Shuji Yamamoto

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

In this article, we introduce and investigate the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that many important constructions studied in K\"unzi's…

General Topology · Mathematics 2019-03-18 Yaé Ulrich Gaba

We introduce finite and symmetric Mordell-Tornheim type of multiple zeta values and give a new approach to the Kaneko-Zagier conjecture stating that the finite and symmetric multiple zeta values satisfy the same relations.

Number Theory · Mathematics 2020-01-30 Henrik Bachmann , Yoshihiro Takeyama , Koji Tasaka

In this paper, we use two different approaches to introduce $q$-analogs of Riemann's zeta function and prove that their values at even integers are related to the $q$-Bernoulli and $q$ Euler's numbers introduced by Ismail and Mansour…

Classical Analysis and ODEs · Mathematics 2020-07-28 Ahmad El-Guindy , Zeinab Mansour

In this paper, we give the values of a certain kind of $q$-multiple zeta functions at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from…

Number Theory · Mathematics 2025-05-15 Takao Komatsu

We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle counterpart' of Hoffman's `odd variant', exhibits nice…

Number Theory · Mathematics 2019-04-18 Masanobu Kaneko , Hirofumi Tsumura

We define a generalisation of the completed Riemann zeta function in several complex variables. It satisfies a functional equation, shuffle product identities, and has simple poles along finitely many hyperplanes, with a recursive structure…

Number Theory · Mathematics 2019-09-09 Francis Brown

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…

Number Theory · Mathematics 2015-06-26 K. Kimoto , N. Kurokawa , S. Matsumoto , M. Wakayama