×

The integral trace form of cyclic extensions of odd prime degree. (English) Zbl 1426.11125

Summary: Let \(L/\mathbb{Q}\) be a cyclic extension of degree \(p\), where \(p\) is an odd unramified prime in \(L/\mathbb {Q}\). An explicit description of the integral trace form \(\mathrm{Tr}_{L/\mathbb{Q}}(x^2)\mid_{\mathfrak{O}_{L}}\), where \(\mathfrak{O}_L\) is the ring of algebraic integers of \(L\), is given, and an application to finding the minima of certain algebraic lattices is presented.

MSC:

11R18 Cyclotomic extensions
11E12 Quadratic forms over global rings and fields
11H31 Lattice packing and covering (number-theoretic aspects)
11H50 Minima of forms
11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
PDF BibTeX XML Cite
Full Text: DOI Euclid