Coleman-Ihara formula

introduction

• 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.

• Chatzistamatiou, Andre. “On Integrality of \(p\)-Adic Iterated Integrals.” arXiv:1501.05760 [math], January 23, 2015. http://arxiv.org/abs/1501.05760.
• Nakamura, Hiroaki, Kenji Sakugawa, and Zdzislaw Wojtkowiak. “Polylogarithmic Analogue of the Coleman-Ihara Formula, I.” arXiv:1410.1045 [math], October 4, 2014. http://arxiv.org/abs/1410.1045.