On 3-class groups of non-Galois cubic fields
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Kiyoaki Iimura (1979)
Acta Arithmetica
Frank III Gerth (1975)
Journal für die reine und angewandte Mathematik
Peter Stevenhagen (1996)
Acta Arithmetica
Toru Nakahara (1982)
Monatshefte für Mathematik
Francisca Cánovas Orvay (1991)
Extracta Mathematicae
Ulrich Halbritter, Michael E. Pohst (2000)
Journal de théorie des nombres de Bordeaux
In this paper we introduce multiplicative lattices in and determine finite unions of suitable simplices as fundamental domains for sublattices of finite index. For this we define cyclic non-negative bases in arbitrary lattices. These bases are then used to calculate Shintani cones in totally real algebraic number fields. We mainly concentrate our considerations to lattices in two and three dimensions corresponding to cubic and quartic fields.
Hamid Ben Yakkou, Jalal Didi (2024)
Mathematica Bohemica
Let be a pure number field generated by a complex root of a monic irreducible polynomial , where , , are three positive natural integers. The purpose of this paper is to study the monogenity of . Our results are illustrated by some examples.
Lhoussain El Fadil (2022)
Commentationes Mathematicae Universitatis Carolinae
Let be a number field generated by a complex root of a monic irreducible polynomial , , is a square free rational integer. We prove that if or and , then the number field is monogenic. If or , then the number field is not monogenic.
Mohammed Sahmoudi, Mohammed Elhassani Charkani (2023)
Mathematica Bohemica
Let be an extension of a number field , where satisfies the monic irreducible polynomial of prime degree belonging to ( is the ring of integers of ). The purpose of this paper is to study the monogenity of over by a simple and practical version of Dedekind’s criterion characterizing the existence of power integral bases over an arbitrary Dedekind ring by using the Gauss valuation and the index ideal. As an illustration, we determine an integral basis of a pure nonic field with a...
Bernadette Deshommes (1989)
Journal für die reine und angewandte Mathematik
Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini (2021)
Commentationes Mathematicae Universitatis Carolinae
Let be a square free integer and . In the present work we determine all the fields such that the -class group, , of is of type or .
Ehud De Shalit, Eyal Z. Goren (1997)
Annales de l'institut Fourier
We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.
Eiji Yoshida (2003)
Acta Arithmetica
H.G. Grundman (1991)
Manuscripta mathematica
Scarowsky, Manny, Boyarsky, Abraham (1986)
International Journal of Mathematics and Mathematical Sciences
Wolfgang Müller (1988)
Monatshefte für Mathematik
Jun Ho Lee, Stéphane R. Louboutin (2014)
Acta Arithmetica
Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic polynomials...
Spearman, Blair K., Williams, Kenneth S. (2004)
International Journal of Mathematics and Mathematical Sciences
Haiyan Zhou (2010)
Acta Arithmetica
E. Thomas, A.T. Vasquez (1980)
Mathematische Annalen
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