| eBook ISBN: | 978-1-61444-010-9 |
| Product Code: | CAR/10.E |
| List Price: | $55.00 |
| MAA Member Price: | $41.25 |
| AMS Member Price: | $41.25 |
| eBook ISBN: | 978-1-61444-010-9 |
| Product Code: | CAR/10.E |
| List Price: | $55.00 |
| MAA Member Price: | $41.25 |
| AMS Member Price: | $41.25 |
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Book DetailsThe Carus Mathematical MonographsVolume: 10; 1950; 212 pp
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.
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Table of Contents
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Chapters
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Chapter I. Forms with real coefficients
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Chapter II. Forms with $p$-adic coefficients
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Chapter III. Forms with rational coefficients
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Chapter IV. Forms with coefficients in $R(p)$
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Chapter V. Genera and semi-equivalence
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Chapter VI. Representations by forms
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Chapter VII. Binary forms
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Chapter VIII. Ternary quadratic forms
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Additional Material
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Reviews
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This excellent monograph gives an introduction to the arithmetic parts of the theory of quadratic forms in self-contained 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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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
-
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 semi-equivalence
-
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 self-contained 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
