On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field

Fumiya Amano, Yasushi Mizusawa, Masanori Morishita

研究成果: ジャーナルへの寄稿記事

1 引用 (Scopus)

抄録

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field Q(-3), following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei’s triple symbol, and describes the decomposition law of a prime in a mod 3 Heisenberg extension of degree 27 over Q(-3) with restricted ramification, which we construct concretely in the form similar to Rédei’s dihedral extension over Q. We also give a cohomological interpretation of our symbols by triple Massey products in Galois cohomology.

元の言語英語
記事番号7
ジャーナルResearch in Number Theory
4
発行部数1
DOI
出版物ステータス出版済み - 3 1 2018

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Number field
Invariant
Galois Cohomology
Ramification
Knot
Analogy
Decompose
Generalise

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

これを引用

On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field. / Amano, Fumiya; Mizusawa, Yasushi; Morishita, Masanori.

:: Research in Number Theory, 巻 4, 番号 1, 7, 01.03.2018.

研究成果: ジャーナルへの寄稿記事

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