Polylogarithmic analogue of the Coleman-Ihara formula, I
Résumé
The Coleman-Ihara formula expresses Soule's p-adic characters restricted to p-local Galois group as the Coates-Wiles homomorphism multiplied by p-adic L-values at positive integers. In this paper, we show an analogous formula that ℓ-adic polylogarithmic characters for ℓ=p restrict to the Coates-Wiles homomorphism multiplied by Coleman's p-adic polylogarithms at any roots of unity of order prime to p.