3 papers
math.NT2026
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…
math.NT2023
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…
math.NT2023
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…