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On mod 3 triple Milnor invariants and tr...

Amano, Fumiya...

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On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field by Amano, Fumiya ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	06-09-2023
Summary	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 R\'{e}dei'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 R\'{e}dei's dihedral extension over $\mathbb{Q}$. We also give a cohomological interpretation of our symbols by triple Massey products in Galois cohomology.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1412.6894

Citation

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AMA 11th EditionReferences

Amano, Fumiya. On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field. Australian National University. September 06, 2023. Accessed September 20, 2024. https://online.provdatabase.com/cite/24111

APA 7th EditionReferences

Amano, Fumiya. (2023). On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field. Australian National University. https://online.provdatabase.com/cite/24111

Chicago 17th EditionReferences

Amano, Fumiya. On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field. Australian National University. 2023. https://online.provdatabase.com/cite/24111

HarvardReferences

Amano, Fumiya. (2023). On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/24111. (Accessed 20 September 2024).

Harvard AustraliaReferences

Amano, Fumiya, 2023, On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field, Australian National University, viewed 20 September 2024, <https://online.provdatabase.com/cite/24111>

MLA 9th EditionWorks Cited

Amano, Fumiya. On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/24111.

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