The Determination Of Some Quaternary Quadratic Forms Which Represent All Positive Integers
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The Determination of All Quaternary Quadratic Forms which Represent Every Positive Integer
Author | : David Clarence Morrow |
Publisher | : |
Total Pages | : 628 |
Release | : 1928 |
Genre | : Forms, Quadratic |
ISBN | : |
Determination of All Classes of Positive Quartenary Quadratic Forms which Represent All (positive) Integers
Author | : Margaret F. Willerding |
Publisher | : |
Total Pages | : 38 |
Release | : 1947 |
Genre | : Forms, Quadratic |
ISBN | : |
Integral Quadratic Forms and Lattices
Author | : Myung-Hwan Kim |
Publisher | : American Mathematical Soc. |
Total Pages | : 314 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821819496 |
This volume presents the proceedings of an international conference held at Seoul National University (Korea). Talks covered recent developments in diverse areas related to the theory of integral quadratic forms and hermitian forms, local densities, linear relations and congruences of theta series, zeta functions of prehomogeneous vector spaces, lattices with maximal finite matrix groups, globally irreducible lattices, Mordell-Weil lattices, and more. Articles in the volume represent expository lectures by leading experts on recent developments in the field. The book offers a comprehensive introduction to the current state of knowledge in the arithmetic theory of quadratic forms and provides active directions of research with new results. Topics addressed in the volume emphasize connections with related fields, such as group theory, arithmetic geometry, analytic number theory, and modular forms. The book is an excellent introductory guide for students as well as a rich reference source for researchers.
Quaternary Quadratic Forms
Author | : Gordon L. Nipp |
Publisher | : Springer Science & Business Media |
Total Pages | : 160 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461231809 |
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.
Algebraic and Arithmetic Theory of Quadratic Forms
Author | : Ricardo Baeza |
Publisher | : American Mathematical Soc. |
Total Pages | : 364 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 082183441X |
This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.
On the Number of Representations by Positive-definite Integer-valued Quaternary Quadratic Forms
Author | : Haochen Wu |
Publisher | : |
Total Pages | : 0 |
Release | : 2021 |
Genre | : |
ISBN | : |
Let {Q1, Q2, . . . , Q[subscript s]} be a finite set of positive-definite integer-valued quaternary quadratic forms. We show that there exists a primitive positive-definite integer-valued quaternary quadratic form Q and a positive integer n such that Q represents n more times than Q[subscript i] for all 1 ≤ i ≤ s.
The Arithmetic Theory of Quadratic Forms
Author | : Burton W Jones |
Publisher | : American Mathematical Soc. |
Total Pages | : 212 |
Release | : 1950-12-31 |
Genre | : Forms, Binary |
ISBN | : 1614440107 |
This monograph presents the central ideas of the arithmetic theory of quadratic forms in self-contained form, assuming only knowledge of the fundamentals of matric theory and the theory of numbers. Pertinent concepts of p -adic numbers and quadratic ideals are introduced. It would have been possible to avoid these concepts, but the theory gains elegance as well as breadth by the introduction of such relationships. Some results, and many of the methods, are here presented for the first time. The development begins with the classical theory in the field of reals from the point of view of representation theory; for in these terms, many of the later objectives and methods may be revealed. The successive chapters gradually narrow the fields and rings until one has the tools at hand to deal with the classical problems in the ring of rational integers. The analytic theory of quadratic forms is not dealt with because of the delicate analysis involved. However, some of the more important results are stated and references are given.
History of the Theory of Numbers, Volume III
Author | : Leonard Eugene Dickson |
Publisher | : Courier Corporation |
Total Pages | : 325 |
Release | : 2005-06-03 |
Genre | : Mathematics |
ISBN | : 0486442349 |
The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This final volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to quadratic and higher forms. It can be read independently of the preceding volumes, which explore divisibility and primality and diophantine analysis. Topics include reduction and equivalence of binary quadratic forms and representation of integers; composition of binary quadratic forms; the composition of orders and genera; irregular determinants; classes of binary quadratic forms with integral coefficients; binary quadratic forms whose coefficients are complete integers or integers of a field; classes of binary quadratic forms with complex integral coefficients; ternary and quaternary quadratic forms; cubic forms in three or more variables; binary hermitian forms; bilinear forms, matrices, and linear substitutions; congruencial theory of forms; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.
Number Theory
Author | : H. Kisilevsky |
Publisher | : American Mathematical Soc. |
Total Pages | : 332 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821870310 |
This volume contains a collection of articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathematiques (CRM) at the University of Montreal. The book represents a cross section of current research and new results in number theory. Topics covered include algebraic number theory, analytic number theory, arithmetic algebraic geometry, computational number theory, and Diophantine analysis and approximation. The volume contains both research andexpository papers suitable for graduate students and researchers interested in number theory.