3 papers
math.NT2026
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…
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.NT2025
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 ser…