Publishing type：Research paper (scientific journal)   Publisher：Mathematical Society of Japan (Project Euclid)  

DOI： 10.2969/jmsj/89088908

arXiv

In this paper, we consider infinite-length versions of multiple zeta-star
values. We give several explicit formulas for the infinite-length versions of
multiple zeta-star values. We also discuss the analytic properties of the map
from indices to the infinite-length versions of multiple zeta-star values.

arXiv

Other Link： http://arxiv.org/pdf/2309.09201v2

Publishing type：Research paper (scientific journal)   Publisher：Mathematical Sciences Publishers  

DOI： 10.2140/tunis.2023.5.73

arXiv

Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s11139-022-00658-1

arXiv

Other Link： https://link.springer.com/article/10.1007/s11139-022-00658-1/fulltext.html

Publishing type：Research paper (scientific journal)   Publisher：Mathematical Institute, Tohoku University  

DOI： 10.2748/tmj.20210409

arXiv

Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.jnt.2021.09.014

arXiv

Publishing type：Research paper (scientific journal)   Publisher：The Electronic Journal of Combinatorics  

Recently, Bényi and the second author introduced two combinatorial interpretations for symmetrized poly-Bernoulli polynomials. In the present study, we construct bijections between these combinatorial objects. We also define various combinatorial polynomials and prove that all of these polynomials coincide with symmetrized poly-Bernoulli polynomials.

DOI： 10.37236/10598

arXiv

We consider the symmetric multiple zeta values in $\mathcal{S}_m$ without
modulo $\pi^2$ reduction for indices in which $1$ and $3$ appear alternately.
We investigate those values that can be expressed as a polynomial of the
Riemann zeta values, and give a conjecturally complete list of explicit
formulas for such values.

arXiv

Other Link： http://arxiv.org/pdf/2203.07701v1

Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s00229-020-01191-5

arXiv

Other Link： http://link.springer.com/article/10.1007/s00229-020-01191-5/fulltext.html

Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s11139-020-00341-3

arXiv

Other Link： https://link.springer.com/article/10.1007/s11139-020-00341-3/fulltext.html

Publishing type：Research paper (scientific journal)   Publisher：Institute of Mathematics, Polish Academy of Sciences  

DOI： 10.4064/aa200621-18-5

arXiv

Publishing type：Research paper (scientific journal)   Publisher：Faculty of Mathematics, Kyushu University  

DOI： 10.2206/kyushujm.75.115

arXiv

Publishing type：Research paper (scientific journal)   Publisher：International Press of Boston  

DOI： 10.4310/ajm.2021.v25.n6.a4

arXiv

By developing various techniques of mould theory, we introduce
$\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal } }$, a mould theoretic
formulation of Drinfeld's associator set. We give a mould-theoretical
generalization of the result that associator relations imply double shuffle
relations, namely, we explain that
$\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal } }$ is embedded to Ecalle's
set $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}\ast\mathsf{is } }$ which is a mould
theoretic version of Racinet's double shuffle set.

arXiv

Other Link： http://arxiv.org/pdf/2312.15423v1

The $t$-adic symmetric multiple zeta value is a generalization of the
symmetric multiple zeta value from the perspective of the Kaneko-Zagier
conjecture. In this paper, we introduce a further generalization with a new
parameter $s$, which we call the $(s,t)$-adic symmetric multiple zeta value.
Then, the $(s,t)$-adic version of the $t$-adic double shuffle relations,
duality and cyclic sum formula are established. A finite counterpart of the
$(s,t)$-adic symmetric multiple zeta value is also discussed.

arXiv

Other Link： http://arxiv.org/pdf/2311.00473v1

In this paper, we investigate an asymptotic behavior of the double zeta
function of Euler-Zagier type for indices with large negative real parts.

arXiv

Other Link： http://arxiv.org/pdf/2303.04650v1

We show that the level 2 case of the cyclotomic Grothendieck-Teichm\"{u}ller
groups introduced by Enriquez coincides with the motivic Galois group of mixed
Tate motives over $\mathbb{Z}[1/2]$.

arXiv

Other Link： http://arxiv.org/pdf/2301.04064v1

In 1998, Borwein, Bradley, Broadhurst and Lison\v{e}k posed two families of
conjectural identities among multiple zeta values, later generalized by
Charlton using his alternating block notation. In this paper, we prove a new
class of identities among multiple zeta values that simultaneously resolve and
generalize these conjectures.

arXiv

Other Link： http://arxiv.org/pdf/2206.03458v1

Gangl, Kaneko, and Zagier gave explicit linear relations among double zeta
values of odd indices coming from the period polynomials of modular forms for
${\rm SL}(2,\mathbb{Z})$. In this paper, we generalize their result to the
linear relations among colored double zeta values of level $N$ coming from the
modular forms for level $N$ congruence subgroups.

arXiv

Other Link： http://arxiv.org/pdf/2205.08507v1