Exemples de plongements d'extensions galoisiennes
Existence et construction des extensions galoisiennes et non-abéliennes de degré 8 d'un corps de caractéristique differente de 2.
Existence of an unramified cyclic extension and congruence conditions
Existence of and computation of integral bases
Existentially closed domains with radical relations.
Existenz unendlicher algebraischer Zahlkörper, über denen jedes Einbettungsproblem lösbar ist.
Explicit Brauer induction.
Explicit construction of integral bases of radical function fields
We give an explicit construction of an integral basis for a radical function field , where , under the assumptions and . The field discriminant of is also computed. We explain why these questions are substantially easier than the corresponding ones in number fields. Some formulae for the -signatures of a radical function field are also discussed in this paper.
Explicit decomposition of a rational prime in a cubic field.
Explicit form of the modular equation.
Explicit forms of Kummer's complementary theorems to his law of quintic reciprocity.
Explicit global function fields over the binary field with many rational places
Explicit upper bounds for |L(1,χ)| for primitive even Dirichlet characters
Explicit upper bounds for the average order of and application to class number.
Explizite Darstellungen von Einheiten und ihre Anwendung auf Mehrklassigkeitsfragen bei reell-quadratischen Zahlkörpern. II.
Explizite Darstellungen von Einheiten und ihre Anwendungen auf Mehrklassigkeitsfragen bei reell-quadratischen Zahlkörpern. I. Explizite Darstellungen von Einheiten reell-quadratischer Zahlkörper.
Explizite Präsentation gewisser Hilbertscher Modulgruppen durch Erzeugende und Relationen.
Exponent of class group of certain imaginary quadratic fields
Let be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form whose ideal class group has an element of order . This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.
Exponential sums associated with algebraic number fields.
Exponential sums associated with the Dedekind zeta-functions.