Trace form via cyclotomic fields

Authors

DOI:

https://doi.org/10.5902/2179460X85207

Keywords:

Trace form, Algebraic lattice, Cyclotomic field

Abstract

Let n ≥ 3 be an integer, ζn a primitive nth root of unity, and K the cyclotomic field Q(ζn). In this paper, we present an explicit description of the integral trace form TrK(αxx), where α, x ∈ K and x is the complex conjugate of x. Furthermore, we present constructions of algebraic lattices via the twisted canonical homomorphism with optimal center density in dimensions 2, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2, 4, 6, 8 and K12.

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Author Biographies

Antonio Aparecido de Andrade, Universidade Estadual Paulista (Unesp)

Graduation in Mathematics by the Instituto de Biocências, Letras e Ciências Exatas de São José do Rio Preto (1984) and PhD in Eletrical Engineering by the Universidade Estadual de Campinas (1996). Professor at the Departamento de Matemática de Instituto de Biociências, Letras e Ciências Exatas of the Universidade Federal Paulista Júlio de Mesquita Filho (Unesp), campus São José do Rio Preto (SP).

Agnaldo José Ferrari, Universidade Estadual Paulista (Unesp)

Agnaldo José Ferrari is Professor at Department of Mathematics, School of Sicences, São Paulo State University (UNESP ) at Bauru - SP.

References

Andrade, A. A., Ferrari, A. J., Benedito, C. W. O., and Costa, S. I. R. (2010). Constructions of algebraic lattices. Computational & Applied Mathematics, 22(3), 493-505.

Conway, J. H. and Sloane, N. J. A. (1998). Sphere packings, latices and groups. Springer- Verlag, 2nd edition.

Ferrari, A. J., Andrade, A. A., Araujo, R. R., and Interlando, J. C. (2020). Trace form of certain subfields of cyclotomic fields and applications. Journal of Algebra Combinatorics Discrete Structures and Applications, 7(2), 141-160.

Interlando, J. C., Neto, T. P. N., Rodrigues, T. M., and Lopes, J. O. D. (2015). A note on the integral trace form in cyclotomic fields. Jounal of Algebra and Applications, 25(5), 1550045-53.

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Published

2024-12-13

How to Cite

Andrade, A. A. de, & Ferrari, A. J. (2024). Trace form via cyclotomic fields. Ciência E Natura, 46, e85207. https://doi.org/10.5902/2179460X85207

Issue

Vol. 46 (2024): Publicação contínua

Section

Mathematics

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