12 papers
Lie algebras for multiple Eisenstein series and multiple q-zeta values
Henrik Bachmann, Hanamichi Kawamura
Racinet's double shuffle Lie algebra encodes the double shuffle relations of multiple zeta values. We study two analogues of for multiple Eisens…
Cyclic sum formula for certain parametrized multiple zeta values
Hanamichi Kawamura, Anju Yokoi
Ohno-Wakabayashi's cyclic sum formula for multiple zeta-star values is generalized by Igarashi with one or two parameters. In this article, we give a possible answer for one of his…
Duality on symmetric multiple polylogarithms
Hanamichi Kawamura
There are three kinds of multiple polylogarithms; complex, finite and symmetric. The dualities for the complex and finite cases are known. In this paper, we present proofs of them…
Discrete iterated integrals and cyclic sum formulas
Hanamichi Kawamura
In this paper, we consider a discrete version of iterated integrals by the naive (equally divided) Riemann sum. In particular, basic three formulas for usual iterated integrals are…
Formal sine functions in harmonic algebra
Hanamichi Kawamura
In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical…
On a lifting of -adic symmetric multiple zeta values
Minoru Hirose, Hanamichi Kawamura
The -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 introduc…
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'…
Iterated integrals associated with colored rooted trees
Hanamichi Kawamura
In this paper, we introduce iterated integrals associated with colored rooted trees and give proofs for the shuffle relations for -adic finite and -adic symmetri…
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…
The hypermultiple gamma functions of BM-type
Hanamichi Kawamura
In this paper, we introduce the hypermultiple gamma functions of BM-type and prove the asymptotic expansion of these functions.
Asymptotic Expansions for the multiple gamma functions of Barnes-Milnor type
Hanamichi Kawamura
The classical Stirling's formula gives the asymptotic behavior of the gamma function. Katayama and Ohtsuki generalized this formula for Barnes' multiple gamma functions. In this pa…
The -multiple gamma functions of Barnes-Milnor type
Hanamichi Kawamura
The multiple gamma functions of BM (Barnes-Milnor) type and the -multiple gamma functions have been studied independently. In this paper, we introduce a new generalization of th…