TY - JOUR
T1 - On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field
AU - Amano, Fumiya
AU - Mizusawa, Yasushi
AU - Morishita, Masanori
N1 - Publisher Copyright:
© 2018, SpringerNature.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s40993-018-0100-7
DO - 10.1007/s40993-018-0100-7
M3 - Article
AN - SCOPUS:85041565000
SN - 2363-9555
VL - 4
JO - Research in Number Theory
JF - Research in Number Theory
IS - 1
M1 - 7
ER -