Author: Marta Sved
Publisher:
ISBN:
Category :
Languages : en
Pages : 252
Book Description
Evaluation of Units in Pure Cubic Number Fields
Author: Marta Sved
Publisher:
ISBN:
Category :
Languages : en
Pages : 252
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 252
Book Description
The Class Numbers of Certain Special Pure Cubic Fields
Author: Samuel Thomas Sanders
Publisher:
ISBN:
Category : Number theory
Languages : en
Pages : 384
Book Description
Publisher:
ISBN:
Category : Number theory
Languages : en
Pages : 384
Book Description
The Determination of Units in Real Cyclic Sextic Fields
Author: S. Mäki
Publisher: Springer
ISBN: 3540392424
Category : Mathematics
Languages : en
Pages : 202
Book Description
Publisher: Springer
ISBN: 3540392424
Category : Mathematics
Languages : en
Pages : 202
Book Description
Asymptotics of Cubic Number Fields with Bounded Second Successive Minimum of the Trace Form
Author: Gero Brockschnieder
Publisher: diplom.de
ISBN: 3956363361
Category : Mathematics
Languages : en
Pages : 85
Book Description
Algebraic number fields, particularly of small degree n, have been treated in detail in several publications during the last years. The subject that has been investigated the most is the computation of lists of number fields K with field discriminant d(K) less than or equal to a given bound D and the computation of the minimal value of the discriminant for a given degree n (and often also signature (r1, r2)) of the number fields. The distinct cases of different degrees, as well as the different numbers of real and complex embeddings, respectively, are usually treated independently of each other since each case itself offers a broad set of problems and questions. In some of the cases the applied methods and algorithms have been notably improved over the years. Each value for the degree n of the investigated fields represents a huge and interesting set of problems and questions that can be treated on its own. The case we will concentrate on in this thesis is n = 3. Algebraic number fields of degree 3 are often referred to as cubic fields and, in a way, their investigation is easier than the investigation of higher degree fields since the higher the degree of the field, the higher the number of possible signatures (i.e. combinations of real and complex embeddings of the field). In this thesis, we will concentrate only on totally real cubic fields. Totally real fields are those fields K for which each embedding of K into the complex numbers C has an image that lies inside the real numbers R. The purpose of this thesis is to show that the number of isomorphism classes of cubic fields K whose second successive minima M2(K), as introduced by Minkowski, are less than or equal to a given bound X is asymptotically equal (in X) to the number of cubic polynomials defining these fields modulo a relation P which will be explained in detail.
Publisher: diplom.de
ISBN: 3956363361
Category : Mathematics
Languages : en
Pages : 85
Book Description
Algebraic number fields, particularly of small degree n, have been treated in detail in several publications during the last years. The subject that has been investigated the most is the computation of lists of number fields K with field discriminant d(K) less than or equal to a given bound D and the computation of the minimal value of the discriminant for a given degree n (and often also signature (r1, r2)) of the number fields. The distinct cases of different degrees, as well as the different numbers of real and complex embeddings, respectively, are usually treated independently of each other since each case itself offers a broad set of problems and questions. In some of the cases the applied methods and algorithms have been notably improved over the years. Each value for the degree n of the investigated fields represents a huge and interesting set of problems and questions that can be treated on its own. The case we will concentrate on in this thesis is n = 3. Algebraic number fields of degree 3 are often referred to as cubic fields and, in a way, their investigation is easier than the investigation of higher degree fields since the higher the degree of the field, the higher the number of possible signatures (i.e. combinations of real and complex embeddings of the field). In this thesis, we will concentrate only on totally real cubic fields. Totally real fields are those fields K for which each embedding of K into the complex numbers C has an image that lies inside the real numbers R. The purpose of this thesis is to show that the number of isomorphism classes of cubic fields K whose second successive minima M2(K), as introduced by Minkowski, are less than or equal to a given bound X is asymptotically equal (in X) to the number of cubic polynomials defining these fields modulo a relation P which will be explained in detail.
Fundamental Units in Cubic Number Fields
Author: Ronald Joel Rudman
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 90
Book Description
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 90
Book Description
Quadratic Number Fields
Author: Franz Lemmermeyer
Publisher: Springer Nature
ISBN: 3030786528
Category : Mathematics
Languages : en
Pages : 348
Book Description
This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.
Publisher: Springer Nature
ISBN: 3030786528
Category : Mathematics
Languages : en
Pages : 348
Book Description
This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.
Mathematics of Computation
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 832
Book Description
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 832
Book Description
Orders in Pure Cubic Number Fields
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
Book Description
The Story of Algebraic Numbers in the First Half of the 20th Century
Author: Władysław Narkiewicz
Publisher: Springer
ISBN: 3030037541
Category : Mathematics
Languages : en
Pages : 448
Book Description
The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.
Publisher: Springer
ISBN: 3030037541
Category : Mathematics
Languages : en
Pages : 448
Book Description
The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.
Mathematical Reviews
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 860
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 860
Book Description