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Let be a finite field extension. The Langlands correspondence gives a canonical bijection between the set of equivalence classes of irreducible -dimensional representations of the Weil group of and the set of equivalence classes of irreducible supercuspidal representations of GL. This paper is concerned with the case where . In earlier work, the authors constructed an explicit bijection using a non-Galois tame base change map. If this tame base change satisfies a certain conjectured...
Cet article a pour objectif de présenter un algorithme permettant de montrer, à l’aide d’un ordinateur, l’euclidianité pour la norme du sous-corps réel maximal du corps cyclotomique où , corps totalement réel de degré et de discriminant , et plus précisément de prouver que . La méthode utilisée permet par ailleurs de prouver que pour , on a également (conjecture de H. Cohn et J. Deutsch). Les résultats relatifs à ce cas sont exposés en fin d’article.
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