Soit un produit de polynômes cyclotomiques. Existe-t-il une forme bilinéaire symétrique entière, unimodulaire et définie positive ayant une isométrie de polynôme caractéristique ? Ce travail donne une réponse partielle à cette question.
Several interesting lattices can be realised as over cyclotomic fields : some of the root lattices, the Coxeter-Todd lattice, the Leech lattice, etc. Many of these are in the sense of Quebbemann. The aim of the present paper is to determine the cyclotomic fields over which there exists a modular ideal lattice. We then study an especially simple class of lattices, the ideal lattices of . The paper gives a complete list of modular ideal lattices of trace type defined on cyclotomic fields.
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic to contain a maximal torus of a given type.
Let be a global field of characteristic not 2, and let be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial if and only if such an isometry exists over all the completions of . This gives a partial answer to a question of Milnor.
General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.
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