English
Related papers

Related papers: Multiple zeta values and iterated log-sine integra…

200 papers

We combine the powerful method of Wilf-Zeilberger pairs with systematic theory of multiple zeta values to prove a large number of series identities due to Z.W. Sun, many of them have been long standing conjectures.

Number Theory · Mathematics 2024-12-25 Kam Cheong Au

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

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…

Number Theory · Mathematics 2011-04-21 Masahiro Igarashi

Two classes of relations for multiple zeta values are handled algebraically. A restricted sum formula is proved by Eie, Liaw and Ong. The derivation relation is proved by Ihara, Kaneko and Zagier. In this paper we show the latter implies…

Number Theory · Mathematics 2013-03-05 Tatsushi Tanaka

We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…

Number Theory · Mathematics 2016-04-29 Yasushi Komori , Kohji Matsumoto , Hirofumi Tsumura

In this paper, we show that regularized elliptic multiple zeta values are given by polynomials in elliptic multiple zeta values with admissible indices and special ones whose indices consist of 0 and 1.

Number Theory · Mathematics 2025-04-24 Taichi Katayama

The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper halfplane, eventually multiplied by $z^{s-1}$, along geodesics connecting two cusps. This setting generalizes simultaneously the…

Number Theory · Mathematics 2007-05-23 Yu. I. Manin

For positive integers $i_1,...,i_k$ with $i_1 > 1$, we define the multiple $t$-value $t(i_1,...,i_k)$ as the sum of those terms in the usual infinite series for the multiple zeta value $\zeta(i_1,...,i_k)$ with odd denominators. Like the…

Number Theory · Mathematics 2020-10-14 Michael E. Hoffman

We consider a generalization of elliptic multiple zeta values, which we call twisted elliptic multiple zeta values. These arise as iterated integrals on an elliptic curve from which a rational lattice has been removed. At the cusp, twisted…

High Energy Physics - Theory · Physics 2018-06-26 Johannes Broedel , Nils Matthes , Gregor Richter , Oliver Schlotterer

Recently, a new kind of multiple zeta value level two $T({\bf k})$ (which is called multiple $T$-values) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind of alternating version of multiple $T$-values, and…

Number Theory · Mathematics 2020-06-23 Ce Xu

We first review our previous works of Arakawa and the authors on two, closely related single-variable zeta functions. Their special values at positive and negative integer arguments are respectively multiple zeta values and poly-Bernoulli…

Number Theory · Mathematics 2018-11-20 Masanobu Kaneko , Hirofumi Tsumura

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…

Number Theory · Mathematics 2017-09-26 Kojiro Oyama

In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a F_p-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between…

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

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 prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.

Number Theory · Mathematics 2022-06-03 Masahiro Igarashi

In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta…

Number Theory · Mathematics 2017-01-16 Ce Xu

We present a summary of recent and older results on Bessel integrals and their relation with zeta numbers.

Mathematical Physics · Physics 2014-01-31 Jean Desbois , Stephane Ouvry

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

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

The motivic coaction of multiple zeta values and multiple polylogarithms encodes both structural insights on and computational methods for scattering amplitudes in a variety of quantum field theories and in string theory. In this work, we…

High Energy Physics - Theory · Physics 2026-05-06 Axel Kleinschmidt , Franziska Porkert , Oliver Schlotterer
‹ Prev 1 8 9 10 Next ›