Shin-ichiro Seki

activity

20152026

most citedA new proof of the duality of multiple zeta values and its generalizations

8 citations · 18 across the 23 of their papers we have counts for

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24 papers · 1 filter

math.NT2026

A proof of Hirose's duality conjecture

Shin-ichiro Seki

Hirose formulated a duality conjecture for a $q$ -discretization of iterated integrals on the four-punctured projective line, incorporating word-dependent $q$ -shifts of the paramete…

math.NT2026

Irreducibility of truncations of the Catalan generating function

Shin-ichiro Seki

We prove that, for every positive integer $n$ , the polynomial $C_{0} + C_{1} x + \dots + C_{n} x^{n}$ is irreducible over $Q$ , where $C_{k}$ denotes the $k$ th Catalan number.

math.NT2026

A note on Zlobin's note

Shin-ichiro Seki

We prove several results concerning the arithmetic nature of multiple zeta values related to Zlobin's 2006 note. Our proofs are based on Zagier's theorem and Lindemann's theorem.

math.NT2026

On the $A$ -transcendence of a Champernowne-type constant

Shin-ichiro Seki

Let $p_{n}$ denote the $n$ -th prime. We prove that for every nonzero polynomial $f (x) \in Z [x]$ , there exist infinitely many positive integers $n$ such that $p_{n} ∤ f (n)$ .

math.NT2026

Some results on naive transcendence in the ring of integers modulo infinitely large primes

Toshiki Matsusaka, Shin-ichiro Seki

This paper presents various transcendence results in the ring of integers modulo infinitely large primes $A$ . In the ring $A$ , one can consider two notions of t…

math.NT2026

Diamond lift of Hirose--Sato's formula involving the Hoffman basis

Shin-ichiro Seki

In this paper, we give a new proof of Hirose--Sato's formula for the expansion of $ζ ({2}^{a_{1} - 1}, 3, \dots, {2}^{a_{r} - 1}, 3, {2}^{c - 1}, 1, {2}^{b_{1}}, \dots, 1, {2}^{b_{s}})$ in the H…

math.NT2025

The $Z$ -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 $Z$ -linear combination of $ζ (k_{1}, \dots, k_{r})$ where $k_{i} \geq 2$ . Our proof also yields an explicit algorithm for such an expan…

math.NT2024

A discretization of the iterated integral expression of the multiple polylogarithm

Minoru Hirose, Toshiki Matsusaka, Shin-ichiro Seki

Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the iterated integral expressions of multiple zeta values become discretized. In this paper, we exte…

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.NT2024

A proof of the extended double shuffle relation without using integrals

Shin-ichiro Seki

We present a new proof of the extended double shuffle relation for multiple zeta values which notably does not rely on the use of integrals. This proof is based on a formula recent…

math.NT2024★ 2 cited

On finite analogues of Euler's constant

Masanobu Kaneko, Toshiki Matsusaka, Shin-ichiro Seki

We introduce and study finite analogues of Euler's constant in the same setting as finite multiple zeta values. We define a couple of candidate values from the perspectives of a ``…

math.NT2023

Regular primes, non-Wieferich primes, and finite multiple zeta values of level $N$

Shin-ichiro Seki

We introduce finite multiple zeta values of general level and discuss the relationship between the non-zeroness of these values and regular or non-Wieferich primes. Because it's ch…

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…

math.NT2021

A note on $F_{n}$ -multiple zeta values

Masataka Ono, Kosuke Sakurada, Shin-ichiro Seki

For several evaluations of special values and several relations known only in $A_{n}$ -multiple zeta values or $S_{n}$ -multiple zeta values, we prove that they are u…

math.NT2020★ 1 cited

Constellations in prime elements of number fields

Wataru Kai, Masato Mimura, Akihiro Munemasa +2

Given any number field, we prove that there exist arbitrarily shaped constellations consisting of pairwise non-associate prime elements of the ring of integers. This result extends…

math.NT2020★ 2 cited

Truncated $t$ -adic symmetric multiple zeta values and double shuffle relations

Masataka Ono, Shin-ichiro Seki, Shuji Yamamoto

We study a refinement of the symmetric multiple zeta value, called the $t$ -adic symmetric multiple zeta value, by considering its finite truncation. More precisely, two kinds of re…

math.NT2020

The connector for Double Ohno relation

Minoru Hirose, Nobuo Sato, Shin-ichiro Seki

In this paper, we introduce a new connector which generalizes the connector found by the third author and Yamamoto. The new connector gives a direct proof of the double Ohno relati…

math.NT2018

Bowman-Bradley type theorem for finite multiple zeta values in $A_{2}$

Hideki Murahara, Tomokazu Onozuka, Shin-ichiro Seki

Bowman and Bradley obtained a remarkable formula among multiple zeta values. The formula states that the sum of multiple zeta values for indices which consist of the shuffle of two…

math.NT2018★ 2 cited

Ohno-type identities for multiple harmonic sums

Shin-ichiro Seki, Shuji Yamamoto

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 rela…

math.NT2018★ 8 cited

A new proof of the duality of multiple zeta values and its generalizations

Shin-ichiro Seki, Shuji Yamamoto

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 z…

math.NT2017

Valuations, arithmetic progressions, and prime numbers

Shin-ichiro Seki

In this short note, we give two proofs of the infinitude of primes via valuation theory and give a new proof of the divergence of the sum of prime reciprocals by Roth's theorem and…

math.NT2016★ 2 cited

The $p$ -adic duality for the finite star-multiple polylogarithms

Shin-ichiro Seki

We prove the $p$ -adic duality theorem for the finite star-multiple polylogarithms. That is a generalization of Hoffman's duality theorem for the finite multiple zeta-s…

math.NT2016

Finite and étale polylogarithms

Kenji Sakugawa, Shin-ichiro Seki

We show an explicit formula relating étale polylogarithms introduced by Wojtkowiak and finite polylogarithms introduced by Elbaz-Vincent and Gangl. This formula is an étale analog…

math.NT2015★ 1 cited

On functional equations of finite multiple polylogarithms

Kenji Sakugawa, Shin-ichiro Seki

Recently, several people study finite multiple zeta values (FMZVs) and finite polylogarithms (FPs). In this paper, we introduce finite multiple polylogarithms (FMPs), which are nat…

A proof of Hirose's duality conjecture

Irreducibility of truncations of the Catalan generating function

A note on Zlobin's note

On the A-transcendence of a Champernowne-type constant

Some results on naive transcendence in the ring of integers modulo infinitely large primes

Diamond lift of Hirose--Sato's formula involving the Hoffman basis

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

A discretization of the iterated integral expression of the multiple polylogarithm

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

A proof of the extended double shuffle relation without using integrals

On finite analogues of Euler's constant

Regular primes, non-Wieferich primes, and finite multiple zeta values of level N

Multivariable connected sums and multiple polylogarithms

A note on Fn​-multiple zeta values

Constellations in prime elements of number fields

Truncated t-adic symmetric multiple zeta values and double shuffle relations

The connector for Double Ohno relation

Bowman-Bradley type theorem for finite multiple zeta values in A2​

Ohno-type identities for multiple harmonic sums

A new proof of the duality of multiple zeta values and its generalizations

Valuations, arithmetic progressions, and prime numbers

The p-adic duality for the finite star-multiple polylogarithms

Finite and étale polylogarithms

On functional equations of finite multiple polylogarithms

On the $A$ -transcendence of a Champernowne-type constant

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

Regular primes, non-Wieferich primes, and finite multiple zeta values of level $N$

A note on $F_{n}$ -multiple zeta values

Truncated $t$ -adic symmetric multiple zeta values and double shuffle relations

Bowman-Bradley type theorem for finite multiple zeta values in $A_{2}$

The $p$ -adic duality for the finite star-multiple polylogarithms