arXiv subjects

Fumiya Amano

Publications and source records attributed to Fumiya Amano.

2 recordsLinked to original sources

arXiv2018

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

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $\mathbb{Q}(\sqrt{-3})$, 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 $\mathbb{Q}(\sqrt{-3})$ with restricted ramification, which we construct concretely in the form similar to Rédei's dihedral extension over $\mathbb{Q}$. We also give a cohomological interpretation of our symbols by triple Massey products in Galois cohomology.

math.NT↗

arXiv2013

On a certain nilpotent extension over Q of degree 64 and the 4-th multiple residue symbol

In this paper, we introduce the 4-th multiple residue symbol $[p_1, p_2, p_3, p_4]$ for certain four prime numbers $p_1, p_2, p_3, p_4$, which extends the Legendre symbol and the Rédei triple symbol in a natural manner. For this we construct concretely a certain nilpotent extension K over Q of degree 64, where ramified prime numbers are $p_1$, $p_2$ and $p_3$, such that the symbol $[p_1, p_2, p_3, p_4]$ describes the decomposition law of $p_4$ in the extension K/Q. We then establish the relation of our symbol and the 4-th arithmetic Milnor invariant (an arithmetic analogue of the 4-th order linking number).

math.NT↗