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

Fumiya Amano, Yasushi Mizusawa, Masanori Morishita

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number7
JournalResearch in Number Theory
Volume4
Issue number1
DOIs
Publication statusPublished - Mar 1 2018

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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