On distribution formulas for complex and $\ell$-adic polylogarithms

Abstract

We study an $\ell$-adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors. As a goal, we obtain a notion of certain universal Kummer-Heisenberg measures that enable interpolating the $\ell$-adic polylogarithmic distribution relations for all degrees.

This article has appeared in the proceedings volume "Periods in Quantum Field Theory and Arithmetic" (J.~Burgos Gil, K.~Ebrahimi-Fard, H.~Gangl eds), [Conference proceedings ICMAT-MZV 2014] Springer Proceedings in Mathematics \& Statistics {\bf 314} (2020), pp.593--619

References in corpus (1)

• Polylogarithmic analogue of the Coleman-Ihara formula, I

Cited by in corpus (1)

• Landen's trilogarithm functional equation and $\ell$-adic Galois multiple polylogarithms