arXiv subjects
Publications and source records attributed to Hanamichi Kawamura.
Brown's lifting procedure shows that one can solve the double shuffle equations modulo products from solutions of linearized ones. In this paper, we reveal that it is described in the framework of Ecalle's dimorphic transportation.
This article is a survey of Ecalle's theory of flexion units. In particular, we provide complete proofs of several key assertions that were stated without proof in Ecalle's original works.
This paper gives a completed proof of Ecalle's senary relation in the original form. As an application, we obtain another proof of the fact that the double shuffle Lie algebra injects into the Kashiwara--Vergne Lie algebra. We also give two explicit isomorphisms between some dimorphic Lie algebras and their linearized version.
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 addition formula and Pythagorean theorem. By taking their image under a linear map with some conditions, they coincide with the classical sine function. Moreover, we show that one such linear map is obtained from iterated integrals.
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 problems about a generalization with three parameters.
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 via iterated integrals and its symmetric counterpart by a similar method.
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 discritized. Moreover, we proved cyclic sum formulas for discrete iterated integrals. They imply the cyclic sum formula for multiple polylogarithms.
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.
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's identity for the generalized hypergeometric function ${}_{5}F_{4}$. Similar results for interpolated refined symmetric multiple zeta values and half refined symmetric multiple zeta values are also discussed.
In this paper, we introduce iterated integrals associated with colored rooted trees and give proofs for the shuffle relations for $\boldsymbol{p}$-adic finite and $t$-adic symmetric polylogarithms. This method generalizes the theory of the finite multiple zeta values associated with $2$-colored rooted trees introduced by Ono.
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. This identity yields explicit procedures for evaluating multivariable connected sums and for giving relations among special values of multiple polylogarithms. In particular, our class of relations contains Ohno's relations for multiple polylogarithms.
In this paper, we introduce the hypermultiple gamma functions of BM-type and prove the asymptotic expansion of these functions.
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 paper, we further generalize these formulas for the multiple gamma functions of BM (Barnes-Milnor) type.
The multiple gamma functions of BM (Barnes-Milnor) type and the $q$-multiple gamma functions have been studied independently. In this paper, we introduce a new generalization of the multiple gamma functions called the $q$-BM multiple gamma function including those functions and prove some properties the BM multiple gamma functions satisfy for them.