eBook ISBN:  9781614440109 
Product Code:  CAR/10.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
eBook ISBN:  9781614440109 
Product Code:  CAR/10.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 

Book DetailsThe Carus Mathematical MonographsVolume: 10; 1950; 212 pp
This monograph presents the central ideas of the arithmetic theory of quadratic forms in selfcontained 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.

Table of Contents

Chapters

Chapter I. Forms with real coefficients

Chapter II. Forms with $p$adic coefficients

Chapter III. Forms with rational coefficients

Chapter IV. Forms with coefficients in $R(p)$

Chapter V. Genera and semiequivalence

Chapter VI. Representations by forms

Chapter VII. Binary forms

Chapter VIII. Ternary quadratic forms


Additional Material

Reviews

This excellent monograph gives an introduction to the arithmetic parts of the theory of quadratic forms in selfcontained form. It assumes only knowledge of the most elementary facts in the theory of numbers and the theory of matrices and, moreover, it is written in a very clear style. For these reasons it will make easy reading even for beginning students.
H. D. Kloosterman, Mathematical Reviews


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This monograph presents the central ideas of the arithmetic theory of quadratic forms in selfcontained 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.

Chapters

Chapter I. Forms with real coefficients

Chapter II. Forms with $p$adic coefficients

Chapter III. Forms with rational coefficients

Chapter IV. Forms with coefficients in $R(p)$

Chapter V. Genera and semiequivalence

Chapter VI. Representations by forms

Chapter VII. Binary forms

Chapter VIII. Ternary quadratic forms

This excellent monograph gives an introduction to the arithmetic parts of the theory of quadratic forms in selfcontained form. It assumes only knowledge of the most elementary facts in the theory of numbers and the theory of matrices and, moreover, it is written in a very clear style. For these reasons it will make easy reading even for beginning students.
H. D. Kloosterman, Mathematical Reviews