Author: Joshua R. Daniels
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 56
Book Description
On Definite Regular Ternary Quadratic Forms Over Fl[T]
Author: Joshua R. Daniels
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 56
Book Description
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 56
Book Description
Strict Regularity of Positive Definite Ternary Quadratic Forms
Author: Hamdan Alsulaimni
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 206
Book Description
An integral quadratic form is said to be strictly regular if it primitively represents all integers that are primitively represented by its genus. The goal of this dissertation is to extend the systematic investigation of the positive definite ternary primitive integral quadratic forms and lattices that are candidates for strict regularity. An integer that is primitively represented by a genus, but not by some specific form in that genus, is called a primitive exception for that form. So, the strictly regular forms are those forms for which there are no primitive exceptions. Our computations of primitive exceptions for each of the 119 positive definite regular ternary forms which lie in multiple-class genera, and of the companion forms in their genera, show that there are 45 inequivalent such forms that are candidates for strict regularity. We provide a proof of the strict regularity of one of these candidates, bringing the total number of forms for which such proofs are known to 15, and prove partial results on the integers primitively represented by the other form in its genus. The theory of primitive spinor exceptional integers is used to analyze the primitive exceptions for the forms in two other genera known to contain a regular ternary form. In these cases, results are obtained relating the primitive representation of certain integers c by a given form in one of these genera to the primitive representation of the integers 4c and 9c by the forms in the genus.
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 206
Book Description
An integral quadratic form is said to be strictly regular if it primitively represents all integers that are primitively represented by its genus. The goal of this dissertation is to extend the systematic investigation of the positive definite ternary primitive integral quadratic forms and lattices that are candidates for strict regularity. An integer that is primitively represented by a genus, but not by some specific form in that genus, is called a primitive exception for that form. So, the strictly regular forms are those forms for which there are no primitive exceptions. Our computations of primitive exceptions for each of the 119 positive definite regular ternary forms which lie in multiple-class genera, and of the companion forms in their genera, show that there are 45 inequivalent such forms that are candidates for strict regularity. We provide a proof of the strict regularity of one of these candidates, bringing the total number of forms for which such proofs are known to 15, and prove partial results on the integers primitively represented by the other form in its genus. The theory of primitive spinor exceptional integers is used to analyze the primitive exceptions for the forms in two other genera known to contain a regular ternary form. In these cases, results are obtained relating the primitive representation of certain integers c by a given form in one of these genera to the primitive representation of the integers 4c and 9c by the forms in the genus.
Ternary Quadratic Forms and Norms
Author: O. Taussky
Publisher: CRC Press
ISBN: 1000116808
Category : Mathematics
Languages : en
Pages : 152
Book Description
This book covers topics including the Redei-Reichardt theorem, automorphs of ternary quadratic forms, facts concerning rational matrices leading to integral ternary forms representing zero, characteristics polynomials of symmetric matrices, and Gauss' theory of ternary quadratic forms.
Publisher: CRC Press
ISBN: 1000116808
Category : Mathematics
Languages : en
Pages : 152
Book Description
This book covers topics including the Redei-Reichardt theorem, automorphs of ternary quadratic forms, facts concerning rational matrices leading to integral ternary forms representing zero, characteristics polynomials of symmetric matrices, and Gauss' theory of ternary quadratic forms.
On Reduced Positive Definite Ternary Quadratic Forms
Author: Kurt Mahler
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 195
Book Description
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 195
Book Description
On a Property of Positive Definite Ternary Quadratic Forms
Author: Kurt Mahler
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 320
Book Description
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 320
Book Description
The Minima of Indefinite Quaternary Quadratic Forms ...
Author: Alexander Oppenheim
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 76
Book Description
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 76
Book Description
Quadratic and Higher Degree Forms
Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
ISBN: 1461474884
Category : Mathematics
Languages : en
Pages : 303
Book Description
In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.
Publisher: Springer Science & Business Media
ISBN: 1461474884
Category : Mathematics
Languages : en
Pages : 303
Book Description
In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.
Rational Quadratic Forms
Author: John William Scott Cassels
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 444
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 444
Book Description
Representations of Definite Quadratic Forms Over Fq[T]
Author: Daniel Greengard
Publisher:
ISBN:
Category : Equations, Quadratic
Languages : en
Pages : 50
Book Description
Publisher:
ISBN:
Category : Equations, Quadratic
Languages : en
Pages : 50
Book Description
Rational Number Theory in the 20th Century
Author: Władysław Narkiewicz
Publisher: Springer Science & Business Media
ISBN: 0857295322
Category : Mathematics
Languages : en
Pages : 659
Book Description
The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Publisher: Springer Science & Business Media
ISBN: 0857295322
Category : Mathematics
Languages : en
Pages : 659
Book Description
The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.