arXiv subjects

Kentaro Ihara

Publications and source records attributed to Kentaro Ihara.

3 recordsLinked to original sources

arXiv2024

Interpolant of truncated multiple zeta functions

We introduce an analytic function $Ψ(s_1,\ldots,s_r;w)$ that interpolates truncated multiple zeta functions $ζ_N(s_1,\ldots,s_r)$. We represent this interpolant as a Mellin transform of a function $G(q_1,\ldots,q_r;w)$ and, using this expression, give the analytic continuation. Further, the harmonic product relations for $Ψ$ and $G$ are established via relevant Hopf algebra structures, and some properties of the function $G$ are provided.

math.NT↗

arXiv2017

Quasi-shuffle products revisited

Quasi-shuffle products, introduced by the first author, have been useful in studying multiple zeta values and some of their analogues and generalizations. The second author, together with Kajikawa, Ohno, and Okuda, significantly extended the definition of quasi-shuffle algebras so it could be applied to multiple zeta q-values. This article extends some of the algebraic machinery of the first author's original paper to the more general definition, and uses this extension to obtain various algebraic formulas in the quasi-shuffle algebra in a transparent way. Some applications to multiple zeta values, interpolated multiple zeta values, multiple q-zeta values, and multiple polylogarithms are given.

math.QA↗

arXiv2012

Iterated period integrals and multiple Hecke $L$-functions

In this paper we express the multiple Hecke $L$-function in terms of a linear combination of iterated period integrals associated with elliptic cusp forms, which is introduced by Manin around 2004. This expression generalizes the classical formula of Hecke $L$-function obtained by the Mellin transformation of a cusp form. Also the expression gives a way of the analytic continuation of the multipleHecke $L$-function.

math.NT↗