3 citations · 3 across the 5 of their papers we have counts for
5 papers
On the Landen formula for multiple polylogarithms and its -adic Galois analogue
Densuke Shiraishi
In the present paper, we provide an algebraic and geometric proof of the Landen formula for complex multiple polylogarithms originally established by Okuda and Ueno. Our approach e…
Duality-reflection formulas of multiple polylogarithms and their -adic Galois analogues
Densuke Shiraishi
In the present paper, we derive formulas of complex and -adic multiple polylogarithms, which have two aspects: a duality in terms of indexes and a reflection in terms of vari…
Spence-Kummer's trilogarithm functional equation and its underlying geometry
Densuke Shiraishi
In this paper, we investigate the underlying geometry of the Spence--Kummer functional equation for the trilogarithm. Our geometry naturally determines a certain path system on the…
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…
On -adic Galois polylogarithms and triple -th power residue symbols
Densuke Shiraishi
The -adic Galois polylogarithm is an arithmetic function on an absolute Galois group with values in -adic numbers, which arises from Galois actions on -adic étale…