Einheitenberechnung in kubischen Körpern mittels des Jacobi-Perronschen Algorithmus aus der Rechenanlage.
Enumerating quartic dihedral extensions of with signatures
In a previous paper, we have given asymptotic formulas for the number of isomorphism classes of -extensions with discriminant up to a given bound, both when the signature of the extensions is or is not specified. We have also given very efficient exact formulas for this number when the signature is not specified. The aim of this paper is to give such exact formulas when the signature is specified. The problem is complicated by the fact that the ray class characters which appear are not all genus characters....
Étude des normes dans les extensions à groupe de Klein
Euclid's algorithm in complex quartic fields
Explicit decomposition of a rational prime in a cubic field.
Fundamental units for orders in certain cubic number fields.
Fundamental units for orders of unit rank 1 and generated by a unit
Let ε be an algebraic unit for which the rank of the group of units of the order ℤ[ε] is equal to 1. Assume that ε is not a complex root of unity. It is natural to wonder whether ε is a fundamental unit of this order. It turns out that the answer is in general yes, and that a fundamental unit of this order can be explicitly given (as an explicit polynomial in ε) in the rare cases when the answer is no. This paper is a self-contained exposition of the solution to this problem, solution which was...
Fundamental units from the perperiod of a generalized Jacobi-Perron algorithm.
Fundamental units in a family of cubic fields
Let be the maximal order of the cubic field generated by a zero of for , . We prove that is a fundamental pair of units for , if
Galois module structure of units in real biquadratic number fields
Généralisation de la théorie des fractions continues
Generalized Kummer theory and its applications
In this report we study the arithmetic of Rikuna’s generic polynomial for the cyclic group of order and obtain a generalized Kummer theory. It is useful under the condition that and where is a primitive -th root of unity and . In particular, this result with implies the classical Kummer theory. We also present a method for calculating not only the conductor but also the Artin symbols of the cyclic extension which is defined by the Rikuna polynomial.
Global restrictions on ramification in number fields.
Grundeinheiten für einige unendliche Klassen reiner biquadratischer Zahlkörper mit einer Anwendung auf die diophanitsche Gleichung x4 - ay4 = ... c (c = 1, 2, 4 oder 8).
Ideal class groups of cubic cyclic fields
Indivisibility of special values of Dedekind zeta functions of real quadratic fields
Integral Points on Certain Elliptic Curves
Kuroda's class number formula
Lösbare Gleichungen axn - byn = c und Grundeinheiten für einige algebraische Zahlkörper vom Grade n = 3, 4, 6.
Mahler measures in a cubic field
We prove that every cyclic cubic extension of the field of rational numbers contains algebraic numbers which are Mahler measures but not the Mahler measures of algebraic numbers lying in . This extends the result of Schinzel who proved the same statement for every real quadratic field . A corresponding conjecture is made for an arbitrary non-totally complex field and some numerical examples are given. We also show that every natural power of a Mahler measure is a Mahler measure.