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.


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
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