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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…

Number Theory · Mathematics 2021-10-28 Hanamichi Kawamura , Takumi Maesaka , Shin-ichiro Seki

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

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…

Number Theory · Mathematics 2018-08-09 Shin-ichiro Seki , Shuji Yamamoto

A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and depth. Recently weighted sum formulas, which are weighted analogues of the sum…

Number Theory · Mathematics 2013-03-12 Tomoya Machide

We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining…

Number Theory · Mathematics 2019-04-23 Ryota Umezawa

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

The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified…

Number Theory · Mathematics 2011-03-11 Shingo Saito , Tatsushi Tanaka , Noriko Wakabayashi

We prove a sum formula with 4 parameters among finite alternating multiple zeta values which can be regarded as an alternating version of the result of Kamano on finite multiple zeta values.

Number Theory · Mathematics 2022-02-22 Takumi Anzawa

In this paper, we discuss the parity result for multiple Dirichlet series which contains some special values of multiple zeta functions as special cases, Mordell--Tornheim type of multiple zeta values, zeta values of the root systems and so…

Number Theory · Mathematics 2019-09-27 Shin-ya Kadota

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…

Number Theory · Mathematics 2019-11-12 Hideki Murahara , Tomokazu Onozuka

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

Riemann zeta values are generalized to multiple zeta values (MZVs) by use of nested sums, and MZVs are generalized to regularized multiple zeta values (RMZVs) by regularization of divergent infinite series. In the present paper, we prove…

Number Theory · Mathematics 2015-08-26 Tomoya Machide

We provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…

Number Theory · Mathematics 2023-08-22 Henrik Bachmann , Jan-Willem van Ittersum

The theory of finite automata applies to the study on relations of multiple zeta values.

Number Theory · Mathematics 2007-05-23 Sinya Kitani , Eiki Sawada , Kimio Ueno

In this note we introduce multi-interpolated multiple zeta values. We provide a basic decomposition of these objects involving ordered partitions. We also obtain identities for special instances of multi-interpolated multiple zeta values…

Combinatorics · Mathematics 2022-02-04 Markus Kuba

The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples,…

Number Theory · Mathematics 2020-11-11 Nikita Markarian

We introduce a family of linear relations between cell-zeta values that have a form similar to product map relations and jointly with them imply stuffle relations between multiple zeta values.

Algebraic Geometry · Mathematics 2022-09-29 Nikita Markarian

The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.

Number Theory · Mathematics 2021-07-28 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

We prove or conjecture several relations between the multizeta values for positive genus function fields of class number one, focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or…

Number Theory · Mathematics 2020-05-12 José Alejandro Lara Rodríguez , Dinesh S. Thakur

The Newton series which interpolate finite multiple harmonic sums are useful in the study of multiple zeta values (MZV's). In this paper, we prove that these Newton series can be written as multiple series. As an application, we give a…

Number Theory · Mathematics 2009-05-05 Gaku Kawashima