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arXiv · 1410.1045

Polylogarithmic analogue of the Coleman-Ihara formula, I

Hiroaki Nakamura·Kenji Sakugawa·Zdzislaw Wojtkowiak
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Abstract

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 $\ell$-adic polylogarithmic characters for $\ell=p$ restrict to the Coates-Wiles homomorphism multiplied by Coleman's $p$-adic polylogarithms at any roots of unity of order prime to $p$.

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Hiroaki Nakamura, Kenji Sakugawa, Zdzislaw Wojtkowiak. 2014-10-04. Polylogarithmic analogue of the Coleman-Ihara formula, I. https://arxiv.org/abs/1410.1045

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