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math.NT2026

A generating function identity for finite and symmetric multiple zeta values via Dougall's bilateral summation

Takumi Maesaka, Masataka Ono

We establish a generating function identity for finite and symmetric multiple zeta values using Dougall's bilateral summation formula. As an application, we prove a restr…

math.NT2026

A double-sum analogue of Whipple's summation formula and a restricted sum formula for multiple binomial sums

Takumi Maesaka

We prove a double-sum analogue of Whipple's summation formula. As an application, we establish a restricted sum formula for multiple binomial sums, which arise as special…

math.NT2026

An analogue of Hirose's relation for finite multiple harmonic -series at roots of unity

Takumi Maesaka

Recently, Hirose proved an analogue of the linear part of Kawashima's relations for refined symmetric multiple zeta values. In this paper, we establish an analogue of Hirose's rela…

math.NT2026

A unified proof of conjectures on the spaces of multiple -zeta values

Minoru Hirose, Takumi Maesaka, Taiki Watanabe

We prove two conjectures on the spaces generated by multiple -zeta values. More precisely, we show that the spaces and already generate…

math.NT2026

Relations and Derivatives of Multiple Eisenstein Series

Henrik Bachmann, Hayato Kanno, Takumi Maesaka

In this paper, we study multiple Eisenstein series, which build a natural bridge between the theory of multiple zeta values and modular forms. We prove a large family of relations…

math.NT2025

The -module of multiple zeta values is generated by ones for indices without ones

Minoru Hirose, Takumi Maesaka, Shin-ichiro Seki +1

We prove that every multiple zeta value is a -linear combination of where . Our proof also yields an explicit algorithm for such an expan…

math.NT2024

Deriving two dualities simultaneously from a family of identities for multiple harmonic sums

Takumi Maesaka, Shin-ichiro Seki, Taiki Watanabe

We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called…

math.NT2023

Weighted sum formula for variants of half multiple zeta values

Hanamichi Kawamura, Takumi Maesaka, Masataka Ono

We prove some weighted sum formulas for half multiple zeta values, half finite multiple zeta values, and half symmetric multiple zeta values. The key point of our proof is Dougall'…

math.NT2021

Multivariable connected sums and multiple polylogarithms

Hanamichi Kawamura, Takumi Maesaka, Shin-ichiro Seki

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. Th…