7 papers
On the -transcendence of a Champernowne-type constant
Shin-ichiro Seki
Let denote the -th prime. We prove that for every nonzero polynomial , there exist infinitely many positive integers such that .
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 . In the ring , one can consider two notions of t…
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 in the…
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 expa…
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 ``…
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…