著者

Densuke SHIRAISHI

出版者

Faculty of Mathematics, Kyushu University

雑誌

Kyushu Journal of Mathematics (ISSN:13406116)

巻号頁・発行日

vol.75, no.1, pp.95-113, 2021 (Released:2021-06-08)

参考文献数

12

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The ℓ-adic Galois polylogarithm is an arithmetic function on an absolute Galois group with values in ℓ-adic numbers, which arises from Galois actions on ℓ-adic étale paths on ℙ1\{0, 1, ∞}. In the present paper, we discuss a relationship between ℓ-adic Galois polylogarithms and triple ℓth power residue symbols in some special cases studied in a work of Hirano and Morishita [J. Number Theory 198 (2019), 211-238]. We show that a functional equation of ℓ-adic Galois polylogarithms by Nakamura and Wojtkowiak [Non-abelian Fundamental Groups and Iwasawa Theory. Cambridge University Press, 2012, pp. 258-310] implies a reciprocity law of triple ℓth power residue symbols.