Polylogarithmic analogue of the Coleman-Ihara formula, I

Hiroaki Nakamura; Kenji Sakugawa; Zdzislaw Wojtkowiak

Polylogarithmic analogue of the Coleman-Ihara formula, I

Number Theory 2017-03-16 v3

Authors: Hiroaki Nakamura , Kenji Sakugawa , Zdzislaw Wojtkowiak

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 $p$ .

Keywords

coleman-ihara formula polylogarithmic characters p-adic l-values coates-wiles homomorphism galois group roots of unity

Cite

@article{arxiv.1410.1045,
  title  = {Polylogarithmic analogue of the Coleman-Ihara formula, I},
  author = {Hiroaki Nakamura and Kenji Sakugawa and Zdzislaw Wojtkowiak},
  journal= {arXiv preprint arXiv:1410.1045},
  year   = {2017}
}

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