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Related papers: Analytic properties of Ohno function

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The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.

Number Theory · Mathematics 2026-03-03 Anju Yokoi

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

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…

Number Theory · Mathematics 2019-05-14 Minoru Hirose , Hideki Murahara , Shingo Saito

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…

General Mathematics · Mathematics 2014-11-13 Michael A. Idowu

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…

Number Theory · Mathematics 2017-03-30 Zhonghua Li , Chen Qin

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.

Number Theory · Mathematics 2019-02-05 Shin-ichiro Seki , Shuji Yamamoto

Asymptotic relations between zeta functions (such as, $\zeta(s),\,\beta(s)$, and other Dirichlet $L$-functions) and interpolation differences of functions like $\vert y\vert^s$ and their interpolating entire functions of exponential type…

Number Theory · Mathematics 2022-12-26 Michael I. Ganzburg

We consider the problem of complex interpolation of certain Hardy-type subspaces of K\"othe function spaces. For example, suppose $X_0$ and $X_1$ are K\"othe function spaces on the unit circle $\bold T,$ and let $H_{X_0}$ and $H_{X_1}$ be…

Functional Analysis · Mathematics 2016-09-06 Nigel J. Kalton

In this survey article some classical results concerning real interpolation between Hardy spaces are briefly presented and then it is explained how those results can be used to establish Yano-type extrapolation theorems for Hardy spaces.…

Classical Analysis and ODEs · Mathematics 2020-01-28 Odysseas Bakas

With the increasing importance of the Mittag-Leffler function in the physical applications, these days many researchers are studying various generalizations and extensions of the Mittag-Leffler function. In this paper efforts are made to…

Complex Variables · Mathematics 2021-07-20 Ritu Agarwal , Urvashi Purohit Sharma , Ravi P. Agarwal

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…

Number Theory · Mathematics 2023-03-28 Masahiro Igarashi

We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.

Number Theory · Mathematics 2021-06-18 Nobushige Kurokawa , Hidekazu Tanaka

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

The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.

Functional Analysis · Mathematics 2019-03-04 A. R. Mirotin , M. A. Romanova

In this paper, we study specific families of multiple zeta values which closely relate to the linear part of Kawashima's relation. We obtain an explicit basis of these families, and investigate their interpolations to complex functions. As…

Number Theory · Mathematics 2019-10-15 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

We give an explicit formula for the well-known parity result for multiple zeta values as an application of the multitangent functions.

Number Theory · Mathematics 2024-10-03 Minoru Hirose

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in…

Number Theory · Mathematics 2024-04-24 Zhonghua Li , Zhenlu Wang

A Master equation has been previously obtained which allows the analytic integration of a fairly large family of functions provided that they possess simple properties. Here, the properties of this Master equation are explored, by extending…

Classical Analysis and ODEs · Mathematics 2018-10-23 M. L. Glasser , Michael Milgram

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we…

Classical Analysis and ODEs · Mathematics 2010-02-11 L. Baratchart , S. Kupin , V. Lunot , M. Olivi

We have looked at the evaluation of the Riemann Zeta function at odd arguments and have provided a simple formula to approximate the value with exponential convergence. We have compared it with various other formulae present in literature.…

Number Theory · Mathematics 2015-03-19 Srinivasan Arunachalam