20 citations · 33 across the 13 of their papers we have counts for
13 papers
The Grothendieck-Teichmüller group acts on the genus mapping class group with or marked point
Pierre Lochak, Hiroaki Nakamura, Leila Schneps
The goal of this article is to prove that the Grothendieck-Teichmüller group acts on and ,the (full) profinite genus mapping c…
On a two-parameter family of tropical Edwards curves
Hiroaki Nakamura, Rani Sasmita Tarmidi
In this paper, a certain two-parameter family of plane-embeddings of Edwards elliptic curve is introduced to provide explicitly computed tropical curve…
Landen's trilogarithm functional equation and -adic Galois multiple polylogarithms
Hiroaki Nakamura, Densuke Shiraishi
The Galois action on the pro- étale fundamental groupoid of the projective line minus three points with rational base points gives rise to a non-commutative formal power seri…
Demi-shuffle duals of Magnus polynomials in a free associative algebra
Hiroaki Nakamura
We study two linear bases of the free associative algebra : one is formed by the Magnus polynomials of type $(\mathrm{ad}_X^{k_1}Y)\cdots(\mathrm{ad}_…
Lissajous 3-braids
Eiko Kin, Hiroaki Nakamura, Hiroyuki Ogawa
We classify 3-braids arising from collision-free choreographic motions of 3 bodies on Lissajous plane curves, and present a parametrization in terms of levels and (Christoffel) slo…
On generalized median triangles and tracing orbits
Hiroaki Nakamura, Hiroyuki Ogawa
We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices…
The automorphism groups of the profinite braid groups
Arata Minamide, Hiroaki Nakamura
In this paper we determine the automorphism groups of the profinite braid groups with four or more strings in terms of the profinite Grothendieck-Teichmüller group.
A family of geometric operators on triangles with two complex variables
Hiroaki Nakamura, Hiroyuki Ogawa
Given a plane triangle , one can construct a new triangle whose vertices are intersections of two cevian triples of . We extend the family of operators by c…
On adelic Hurwitz zeta measures
Hiroaki Nakamura, Zdzislaw Wojtkowiak
In this paper we construct a $\hat\mathbb{Z}$-valued measure on $\hat\mathbb{Z}$ which interpolates -adic Hurwitz zeta functions for all .
On distribution formulas for complex and -adic polylogarithms
Hiroaki Nakamura, Zdzislaw Wojtkowiak
We study an -adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors. As a goal, we obtain a no…
Polylogarithmic analogue of the Coleman-Ihara formula, I
Hiroaki Nakamura, Kenji Sakugawa, Zdzislaw Wojtkowiak
The Coleman-Ihara formula expresses Soule's -adic characters restricted to -local Galois group as the Coates-Wiles homomorphism multiplied by -adic -values at positive…
Some IHX type relations on trivalent graphs and symplectic representation theory
Stavros Garoufalidis, Hiroaki Nakamura
We consider several algebras that arise in the study of the mapping class group (by means of topology and Hodge theory) and describe their symplectic-invariant parts in terms of al…
Universal low-temperature properties of quantum and classical ferromagnetic chains
Minoru Takahashi, Hiroaki Nakamura, Subir Sachdev
We identify the critical theory controlling the universal, low temperature, macroscopic properties of both quantum and classical ferromagnetic chains. The theory is the quantum mec…