Primes of the form p = x² + ny² : Fermat, class field theory, and complex multiplication /
The basic question of the whole book, which we formulate as follows: Basic Question 0.1. Given a positive integer n, which primes p can be expressed in the form p = x² + ny² where x and y are integers? This book has several goals. The first, to answer the basic question, has already been stated. A s...
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| Format: | eBook |
| Language: | English |
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Hoboken, New Jersey :
John Wiley & Sons, Inc.,
[2013]
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| Edition: | Second edition. |
| Series: | Pure and applied mathematics (John Wiley & Sons : Unnumbered)
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | The basic question of the whole book, which we formulate as follows: Basic Question 0.1. Given a positive integer n, which primes p can be expressed in the form p = x² + ny² where x and y are integers? This book has several goals. The first, to answer the basic question, has already been stated. A second goal is to bridge the gap between elementary number theory and class field theory. Although our basic question is simple enough to be stated in any beginning course in number theory, we will see that its solution is intimately bound up with higher reciprocity laws and class field theory. A related goal is to provide a well-motivated introduction to the classical formulation of class field theory. This will be done by carefully stating the basic theorems and illustrating their power in various concrete situations. |
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| Item Description: | Originally published: Primes of the form x² + ny², 1989. |
| Physical Description: | 1 online resource (xvi, 359 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 335-342), further reading bibliography (pages 343-346), and index. |
| ISBN: | 9781118400746 1118400747 9781118400739 1118400739 9781118400753 1118400755 1322078289 9781322078281 1118390180 9781118390184 |