Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 54, Number 1 (2017), 55-74.
Polylogarithmic analogue of the Coleman-Ihara formula, I
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 $p$.
Osaka J. Math., Volume 54, Number 1 (2017), 55-74.
First available in Project Euclid: 3 March 2017
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G55: Polylogarithms and relations with $K$-theory
Secondary: 14H30: Coverings, fundamental group [See also 14E20, 14F35] 11S31: Class field theory; $p$-adic formal groups [See also 14L05] 11R18: Cyclotomic extensions
Nakamura, Hiroaki; Sakugawa, Kenji; Wojtkowiak, Zdzisław. Polylogarithmic analogue of the Coleman-Ihara formula, I. Osaka J. Math. 54 (2017), no. 1, 55--74. https://projecteuclid.org/euclid.ojm/1488531784