Serre's A Course in Arithmetic is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level.From the reviews: "... The book is carefully written - in particular very much self-contained. As was the intention of the author, it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last chapter, more difficult for the beginner, is an introduction to contemporary problems." American Scientist
Here is a modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms.From the reviews: "The book is carefully written--in particular very much self-contained...it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last chapter, more difficult for the beginner, is an introduction to contemporary problems."---AMERICAN SCIENTIST| Preface |
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| Part I--Algebraic Methods |
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3 | (8) |
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3 | (2) |
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Equations over a finite field |
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5 | (1) |
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Quadratic reciprocity law |
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6 | (5) |
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Another proof of the quadratic reciprocity law |
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9 | (2) |
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11 | (8) |
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The ring Zp and the field Qp |
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11 | (2) |
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13 | (2) |
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The multiplicative group of Qp |
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15 | (4) |
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19 | (8) |
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19 | (4) |
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23 | (4) |
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Quadratic forms over Qp and over Q |
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27 | (21) |
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27 | (8) |
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35 | (6) |
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41 | (7) |
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45 | (3) |
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Integral quadratic forms with discriminant ± 1 |
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48 | (13) |
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48 | (4) |
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52 | (3) |
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55 | (6) |
| Part II---Analytic Methods |
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The theorem on arithmetic progressions |
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61 | (16) |
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Characters of finite abelian groups |
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61 | (3) |
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64 | (4) |
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Zeta function and L functions |
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68 | (5) |
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Density and Dirichlet theorem |
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73 | (4) |
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77 | (35) |
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77 | (2) |
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79 | (5) |
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The space of modular forms |
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84 | (6) |
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90 | (8) |
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98 | (8) |
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106 | (6) |
| Bibliography |
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112 | (2) |
| Index of Definitions |
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114 | (1) |
| Index of Notations |
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115 | |
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