Jun-ichi Okuda, Kimio Ueno
Ohno's relation gives a large family of relations of the multiple zeta values. We shall show functional relations of generating functions of Ohno's relation. With these relations we present a new proof of Ohno's relation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Ohno's relation is a well-known relation among multiple zeta values.In this paper, we prove Ohno-type relation for finite multiple zeta values, which is conjectured by Kaneko.As a corollary, we give an alternative proof of the sum formula for finite multiple zeta values, which was first proved by Saito and Wakabayashi.
The Ohno relation is a well-known relation among multiple zeta values. Hirose, Onozuka, Sato, and the author investigated the sum related to the Ohno relation and presented two types of new relations and five conjectural formulas. This paper proves one of these formulas.
We establish finite analogues of the identities known as the Aoki-Ohno relation and the Le-Murakami relation in the theory of multiple zeta values. We use an explicit form of a generating series given by Aoki and Ohno.
The Ohno relation is a well known relation in the theory of multiple zeta values. Recently, Seki and Yamamoto introduced a connector method and gave its succinct proof. On the other hand, Igarashi obtained the generalization of the Ohno relation for parametrized multiple zeta series. In this paper, we give new connectors to simplify his proof.
Ohno's relation is a well-known family of relations among multiple zeta values, which can naturally be regarded as a type of duality for a certain power series which we call an Ohno sum. In this paper, we investigate $\mathbb{Q}$-linear relations among Ohno sums which are not contained in Ohno's relation. We prove two new families of such relations, and pose several further conjectural families of such relations.
We prove the Ohno-type relation for the interpolated multiple zeta values, which was introduced first by Yamamoto. Same type results for finite multiple zeta values are also given. Moreover, these relations give the sum formula for interpolated multiple zeta values and interpolated $\mathcal{F}$-multiple zeta values, which were proved by Yamamoto and Seki, respectively.
Ohno's relation states that a certain sum, which we call an Ohno type sum, of multiple zeta values remains unchanged if we replace the base index by its dual index. In view of Oyama's theorem concerning Ohno type sums of finite and symmetric multiple zeta values, Kaneko looked at Ohno type sums of finite and symmetric multiple zeta-star values and made a conjecture on the generating function for a specific index of depth three. In this paper, we confirm this conjecture and further give a formula for arbitrary indices of depth three.
The Ohno relation for multiple zeta values can be formulated as saying that a certain operator, defined for indices, is invariant under taking duals. In this paper, we generalize the Ohno relation to regularized multiple zeta values by showing that, although the suitably generalized operator is not invariant under taking duals, the relation between its values at an index and at its dual index can be written explicitly in terms of the gamma function.
In this paper, we prove that certain parametrized multiple series which generalize multiple zeta values satisfy the same relation as Ohno's relation for multiple zeta values. This is a parametrized generalization of Ohno's relation for multiple zeta values. By virtue of this generalization, we obtain a certain equivalence between the relation for the parametrized multiple series and its subfamily. As applications of the above results, we obtain some results for multiple zeta values.
Ohno relation for regularized refined symmetric multiple zeta values
本文将 Ohno 关系从精炼对称多重 zeta 值进一步推广到正则化精炼对称多重 zeta 值，即从 $0$ 到 $0$ 的非容许迭代积分情形。
We establish Ohno-type identities for multiple harmonic ($q$-)sums which generalize Hoffman's identity and Bradley's identity. Our result leads to a new proof of the Ohno-type relation for $\mathcal{A}$-finite multiple zeta values recently proved by Hirose, Imatomi, Murahara and Saito. As a further application, we give certain sum formulas for $\mathcal{A}_2$- or $\mathcal{A}_3$-finite multiple zeta values.
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 paper, we give a generalization of Kawasaki and Oyama's results.
Ohno's relation is a generalization of both the sum formula and the duality formula for multiple zeta values. Oyama gave a similar relation for finite multiple zeta values, defined by Kaneko and Zagier. In this paper, we prove relations of similar nature for both multiple zeta-star values and finite multiple zeta-star values. Our proof for multiple zeta-star values uses the linear part of Kawashima's relation.
Ohno's relation is a well known formula among multiple zeta values. In this paper, we present its interpolation to complex functions.
Let $X_0^{\star}(k,n,s)$ denote the sum of all multiple zeta-star values of weight $k$, depth $n$ and height $s$. Kaneko and Ohno conjecture that for any positive integers $m,n,s$ with $m,n\geqslant s$, the difference $(-1)^mX_0^{\star}(m+n+1,n+1,s)-(-1)^nX_0^{\star}(m+n+1,m+1,s)$ can be expressed as a polynomial of zeta values with rational coefficients. We give a proof of this conjecture in this paper.
Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute convergence, give some new expressions, and show new relations of the function. We also give a direct proof of the interpolation of Ohno's relation.
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 relations. The corresponding products are related in terms of duality. In this work we study Zudilin's duality construction in the context of classical multiple zeta values as well as various q-analogs of multiple zeta values. Regarding the former we identify the derivation relation of order two with a Hoffman-Ohno type relation. Then we describe relations bet…
We study for $s\in\N=\{1,2,...\}$ the functions $ξ_{k}(s)=\frac{1}{Γ(s)}\int_{0}^{\infty}\frac{t^{s-1}}{e^t-1}\Li_{k}(1-e^{-t})dt$, and more generally $ξ_{k_1,...,k_r}(s)=\frac{1}{Γ(s)}\int_{0}^{\infty}\frac{t^{s-1}}{e^t-1}\Li_{k_1,...,k_r}(1-e^{-t})dt$, introduced by Arakawa and Kaneko \cite{Arakawa} and relate them with (finite) multiple zeta functions, partially answering a question of \cite{Arakawa}. In particular, we give an alternative proof of a result of Ohno \cite{Ohno2}.
In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of `extra functional equations' involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper we generalize their result by proving a similar identity relating certain degree l fields with Galois groups D_l and F_l respectively, for any odd prime l, and in particular we give ano…
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 formula for these polynomials.
The relationship between the Ohno relation and multiple polylogarithms are discussed. Using this relationship, the algebraic reduction of the Ohno relation is given.
We prove some relations for the $q$-multiple zeta values ($q$MZV). They are $q$-analogues of the cyclic sum formula, the Ohno relation and the Ohno-Zagier relation for the multiple zeta values (MZV). We discuss the problem to determine the dimension of the space spanned by $q$MZV's over $\Q$, and present an application to MZV.
An interpolation of the generalized duality formula for the Schur multiple zeta values to complex functions
本文基于Euler-Zagier型方法，对Schur多重zeta值的广义对偶公式（即Ohno relation）进行插值，并证明该关系对复数成立。
We give a new proof of the duality of multiple zeta values, which makes no use of the iterated integrals. The same method is also applicable to Ohno's relation for ($q$-)multiple zeta values.
Cyclic sum formula for certain parametrized multiple zeta values
本文针对Igarashi推广Ohno-Wakabayashi多重泽塔星值循环和公式后提出的三参数推广问题之一，给出了可能的解答。
In this paper, we introduce a new connector which generalizes the connector found by the third author and Yamamoto. The new connector gives a direct proof of the double Ohno relation recently proved by the first author, the second author, Murahara, and Onozuka. Furthermore, we obtain a simultaneous generalization of the ($q$-)Ohno relation and the ($q$-)double Ohno relation.
We exhibit the double q-shuffle structure for the qMZVs recently introduced by Y. Ohno, J. Okuda and W. Zudilin.
We prove a new class of relations among multiple zeta values (MZV's) which contains Ohno's relation. We also give the formula for the maximal number of independent MZV's of fixed weight, under our new relations. To derive our formula for MZV's we consider the Newton series whose values at non-negative integers are finite multiple harmonic sums.
The derivation relation is a well known relation among multiple zeta values, which was first obtained by Ihara, Kaneko and Zagier. The analogous formula for finite multiple zeta values, which we call the derivation relation for finite multiple zeta values, was conjectured by the third author and proved by the second author. In this paper, we show these two kinds of derivation relations are respectively equivalent to the Ohno type relations for multiple zeta values and finite multiple zeta values. We also reprove these derivation relations in several different ways.
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 generalized duality formula (so called Ohno relation) obtained by the second author. In this article, we will discuss them for the Schur multiple zeta values which are the values at positive integers of the Schur multiple zeta function introduced by the first author, O. Phukswan and Y. Yamasaki.
We show that a duality formula for certain parametrized multiple series yields numerous relations among them. As a result, we obtain a new relation among extended multiple zeta values, which is an extension of Ohno's relation for multiple zeta values. We do the same study also to multiple Hurwitz zeta values, and obtain a new identity for them.
We study the Ohno-Zagier type relation for multiple $t$-values and multiple $t$-star values. We represent the generating function of sums of multiple $t$-(star) values with fixed weight, depth and height in terms of the generalized hypergeometric function $\,_3F_2$. As applications, we get a formula for the generating function of sums of multiple $t$-(star) values of maximal height and a weighted sum formula for sums of multiple $t$-(star) values with fixed weight and depth.
Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of interpolated multiple $q$-zeta values with fixed weight, depth and $i$-height. The functions are systematically expressed in terms of the basic hypergeometric functions. Compared with the result of Ohno and Zagier, our result includes three generalizations: general height, $q$-deformation and $t$-interpolation. As an application, we prove some expected relations f…
Multiple zeta values ending with a fixed string
基于Ohno-Zagier定理的证明，给出固定权重、深度和高度且以给定字符串结尾的所有多重zeta值之和的生成级数表达式，并应用于插值多重zeta值和双zeta值的生成级数。
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 involving multiple zeta star values (MZSV): the Two-one formula conjectured by Ohno and Zudilin, and a few conjectures of Imatomi et al. involving 2-3-2-1 type MZSV, where 2 means some finite string of 2's
In this paper we give a new proof of the Ohno-Nakagawa Theorem using the techniques of $L$-series. By applying Eisenstein's parametrization of binary cubic forms on the one hand, and a class field theory interpretation of Datskovsky \& Wright's Theorem on the other, we reduce the Ohno-Nakagawa Theorem to an identity involving the $L$-series and the truncated $L$-series of quadratic orders. We prove this identity by establishing a general relation among these two types $L$-series.
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 relations for multiple zeta values. Very recently, Zhao generalized this set of MHS identities to strings with repetitions of the above patterns and, as an application, proved the two-one formula for multiple zeta star values conjectured by Ohno and Zudilin. In this paper, we extend our approach to $q$-binomial identities and prove $q$-analogues of two-one formulas…
Refined sum formulas for finite multiple zeta values of level two
本文针对第二层级有限多重zeta值建立了两类精细求和公式，包括一个显式求和公式和一个Ohno--Zagier型关系，并由此推导出固定权重、深度及特殊高度的求和公式。
We introduce a $q$-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple $q$-zeta values satisfy a $q$-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values. Additionally, multiple $q$-zeta values can be viewed as special values of the multiple $q$-polylogarithm, which admits a multiple Jackson $q$-integral representation whose limiting case is the Drinfel'd simplex integral for the ordinary multiple polylogarithm when $q=1$. The multiple Jackson $q$-integral r…
The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler's formula was obtained by Ohno and Zudilin. We generalize it to a weighted sum formula for multiple zeta values of all dimensions.
A q-analogue of symmetric multiple zeta value
本文构造了满足对偶洗牌关系的对称多重zeta值截断版本的q-模拟，借此定义了对称多重zeta值的q-模拟，并证明其满足逆关系、部分对偶洗牌关系及Ohno型关系。
We study special values of finite multiple harmonic q-series at roots of unity. These objects were recently introduced by the authors and it was shown that they have connections to finite and symmetric multiple zeta values and the Kaneko-Zagier conjecture. In this note we give new explicit evaluations for finite multiple harmonic q-series at roots of unity and prove Ohno-Zagier-type relations for them.
A new deformation of multiple zeta value
本文引入了一种带参数$ω$的多重zeta值（MZV）新变形，通过多重积分在$q$MZV的代数框架下定义，并证明了其满足双重洗牌关系及扩展的双重Ohno关系。
We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a byproduct we obtain Ohno-type relations for finite multiple harmonic q-series at a root of unity.
Quasi-shuffle products, introduced by the first author, have been useful in studying multiple zeta values and some of their analogues and generalizations. The second author, together with Kajikawa, Ohno, and Okuda, significantly extended the definition of quasi-shuffle algebras so it could be applied to multiple zeta q-values. This article extends some of the algebraic machinery of the first author's original paper to the more general definition, and uses this extension to obtain various algebraic formulas in the quasi-shuffle algebra in a transparent way. Some applications to multiple zeta va…
We introduce the multivariable connected sum which is a generalization of Seki-Yamamoto's connected sum and prove the fundamental identity for these sums by series manipulation. This identity yields explicit procedures for evaluating multivariable connected sums and for giving relations among special values of multiple polylogarithms. In particular, our class of relations contains Ohno's relations for multiple polylogarithms.
T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an analog of the Arakawa-Kaneko zeta function of Miyagawa-type (defined by T. Miyagawa) and to obtain a relation among Miyagawa-type MZVs. The other is to find a class of zeta functions to which Ito's zeta functions of the case of general index are related.
The derivation relations for multiple zeta values is proved by Ihara, Kaneko and Zagier. We prove its counterpart for finite multiple zeta values.
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 particular, prove the cyclic sum formula, the Bowman-Bradley type formula, and the weighted sum formula. The harmonic relation, the shuffle relation, the duality relation, and the derivation relation are also presented.
Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the symmetric sum formula, the shuffle regularized sum formula, a weighted sum formula and some evaluation formulas with even arguments. All the algebraic relations provided in this paper are deduced from the extended double shuffle relations.
The cyclic relation obtained in a study by Hirose, Murakami, and the first-named author, is a wide class of relations, which includes the well-known cyclic sum formula for multiple zeta and zeta-star values, and the derivation relation for multiple zeta values. In this paper, we present its generalization to complex variables. Our proof includes a new proof of the cyclic relation.
We consider the problem of deducing the duality relation from the extended double shuffle relation for multiple zeta values. Especially we prove that the duality relation for double zeta values and that for the sum of multiple zeta values whose first components are 2's are deduced from the derivation relation, which is known as a subclass of the extended double shuffle relation.
In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums of interpolated multiple zeta values of fixed weight, depth and height is represented by hypergeometric functions, and we discuss some special cases.
Ihara, Kaneko, and Zagier proved the derivation relation for multiple zeta values. The first named author obtained its counterpart for finite multiple zeta values in $\mathcal{A}$. In this paper, we present its generalization in $\mathcal{A}_{n}$.
Some combinatorial aspects of relations between multiple zeta values of depths 2 and 3 and period polynomials are discussed.
In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple zeta values in terms of unit-exponent alternating multiple zeta values. In particular, we prove several conjectures given by Borwein-Bradley-Broadhurst \cite{BBBL1997}, and give some general results. Furthermore, we discuss Kaneko-Yamamoto multiple zeta values, and establish some relations between it and multiple zeta values. Finally, we establish a linear re…
We treat desingularized multiple zeta-functions introduced by Furusho, Komori, Matsumoto and Tsumura. In this paper, we prove functional relations, which are shuffle type product formulae, between desingularized multiple zeta-functions and desingularized values.
Symmetric multiple zeta values (SMZVs) are elements in the ring of all multiple zeta values modulo the ideal generated by $ζ(2)$ introduced by Kaneko-Zagier as counterparts of finite multiple zeta values. It is known that symmetric multiple zeta values satisfy double shuffle relations and duality relations. In this paper, we construct certain lifts of SMZVs which live in the ring generated by all multiple zeta values and $2πi$ as certain iterated integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty\}$ along a certain closed path. We call this lifted values as refined symmetric multiple zeta value…
We show that the duality relation for the sum of multiple zeta values with fixed weight, depth and $k_1$ is deduced from the derivation relations, which was first conjectured by N. Kawasaki and T. Tanaka.
We take another look at the so-called quasi-derivation relations in the theory of multiple zeta values, by giving a certain formula for the quasi-derivation operator. In doing so, we are not only able to prove the quasi-derivation relations in a simpler manner but also give an analog of the quasi-derivation relations for finite multiple zeta values.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。