On Reduced Positive Definite Ternary Quadratic Forms PDF Download

Author: Kurt Mahler
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 195

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Author: Alexander Oppenheim
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 76

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Book Description

Author: O. Taussky
Publisher: CRC Press
ISBN: 1000116808
Category : Mathematics
Languages : en
Pages : 152

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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.

Author: Hamdan Alsulaimni
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 206

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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.

Author: Donald Williamson Pounder
Publisher:
ISBN:
Category :
Languages : en
Pages : 64

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Author: Kurt Mahler
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 320

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Author: National Research Council (U.S.). Committee on tables of positive ternary quadratic forms
Publisher:
ISBN:
Category : Forms, Quadratic
Languages : en
Pages : 58

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Author: G. Barratt
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Gordon L. Nipp
Publisher: Springer Science & Business Media
ISBN: 1461231809
Category : Mathematics
Languages : en
Pages : 160

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Book Description
This book of tables includes a reduced representative of each class of. integral positive definite primitive quaternary quadratic forms through discriminant 1732. The classes are grouped into genera; also included are Hasse symbols, the number of automorphs and the level of each such form, and the mass of each genus. An appendix lists p-adic densities and p-adic Jordan splittings for each genus in the tables for p = 2 and for each odd prime p dividing the discriminant. The book is divided into several sections. The first, an introductory section, contains background material, an explanation of the techniques used to generate the information contained in the tables, a description of the format of the tables, some instructions for computer use, examples, and references. The next section contains a printed version of the tables through discriminant 500, included to allow the reader to peruse at least this much without the inconvenience of making his/her own hard copy via the computer. Because of their special interest, we include tables of discriminants 729 and 1729 at the end of this section. Limitations of space preclude publication of more than this in printed form. A printed appendix through discriminant 500 and for discriminants 729 and 1729 follows. The complete tables and appendix through discriminant 1732 are compressed onto the accompanying 3.5 inch disk, formatted for use in a PC-compatible computer and ready for research use particularly when uploaded to a mainframe. Documentation is included in the Introduction.

Author: J. W. S. Cassels
Publisher: Courier Dover Publications
ISBN: 0486466701
Category : Mathematics
Languages : en
Pages : 429

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Book Description
Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.