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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…

Number Theory · Mathematics 2020-12-15 Ken Kamano , Tomokazu Onozuka

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

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…

Number Theory · Mathematics 2017-01-03 Ce Xu

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…

Number Theory · Mathematics 2018-04-02 Ryota Umezawa

The duality relation is a basic family of linear relations for multiple zeta values. The extended double shuffle relation (EDSR) is one of the families of relations expected to generate all linear relations among multiple zeta values, but…

Number Theory · Mathematics 2022-08-19 Aiki Kimura

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…

Number Theory · Mathematics 2020-09-30 Hideki Murahara

Starting from a recent result expressing the Lerch zeta function as a fractional derivative, we consider further fractional derivatives of the Lerch zeta function with respect to different variables. We establish a partial differential…

Number Theory · Mathematics 2020-06-02 Arran Fernandez , Jean-Daniel Djida

Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a…

Number Theory · Mathematics 2025-07-22 Naho Kawasaki

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 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

Kaneko and Yamamoto introduced a convoluted variant of multiple zeta values (MVZs) around 2016. In this paper, we will first establish some explicit formulas involving these values and their alternating version by using iterated integrals,…

Number Theory · Mathematics 2025-08-06 Ce Xu , Jianqiang Zhao

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

We study relations between multizeta values for function fields introduced by D. Thakur. The F_p-span of Thakur's multizeta values is an algebra (Thakur. Shuffle relations for function field multizeta values). In particular, the product…

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

Kawashima's relation is conjecturally one of the largest classes of relations among multiple zeta values. Gaku Kawashima introduced and studied a certain Newton series, which we call the Kawashima function, and deduced his relation by…

Number Theory · Mathematics 2020-12-01 Masanobu Kaneko , Ce Xu , Shuji Yamamoto

Ihara, Kaneko, and Zagier defined two regularizations of multiple zeta values and proved the regularization theorem that describes the relation between those regularizations. We show that the regularization theorem can be generalized to…

Number Theory · Mathematics 2018-10-31 Minoru Hirose , Hideki Murahara , Shingo Saito

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

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,…

Number Theory · Mathematics 2010-03-18 Li Guo , Bingyong Xie

Multiple $T$-values, a variant of multiple zeta values of level two, were introduced and studied by Kaneko and Tsumura. This paper will introduce iterated log-tangent integrals and discuss their relations with multiple $T$-values. We will…

Number Theory · Mathematics 2023-01-18 Ryota Umezawa

Multiple zeta values are real numbers defined by an infinite series generalizing values of the Riemann zeta function at positive integers. Finite truncations of this series are called multiple harmonic sums and are known to have interesting…

Number Theory · Mathematics 2015-06-12 Julian Rosen

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