A Course in Arithmetic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1973
|
| Schriftenreihe: | Graduate Texts in Mathematics
7 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors |
| Beschreibung: | 1 Online-Ressource (X, 118 p) |
| ISBN: | 9781468498844 9780387900414 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-9884-4 |
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Datensatz im Suchindex
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| author | Serre, Jean-Pierre |
| author_facet | Serre, Jean-Pierre |
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| author_sort | Serre, Jean-Pierre |
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| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-10T01:21:08Z |
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| isbn | 9781468498844 9780387900414 |
| issn | 0072-5285 |
| language | English |
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| spelling | Serre, Jean-Pierre Verfasser aut A Course in Arithmetic by Jean-Pierre Serre New York, NY Springer New York 1973 1 Online-Ressource (X, 118 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 7 0072-5285 This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors Mathematics Number theory Number Theory Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Zahlkörper (DE-588)4067273-6 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s 1\p DE-604 Arithmetik (DE-588)4002919-0 s 2\p DE-604 Algebraische Zahlentheorie (DE-588)4001170-7 s 3\p DE-604 Analytische Zahlentheorie (DE-588)4001870-2 s 4\p DE-604 Zahlkörper (DE-588)4067273-6 s 5\p DE-604 https://doi.org/10.1007/978-1-4684-9884-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Serre, Jean-Pierre A Course in Arithmetic Mathematics Number theory Number Theory Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd Arithmetik (DE-588)4002919-0 gnd Zahlkörper (DE-588)4067273-6 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4001870-2 (DE-588)4001170-7 (DE-588)4002919-0 (DE-588)4067273-6 (DE-588)4067277-3 |
| title | A Course in Arithmetic |
| title_auth | A Course in Arithmetic |
| title_exact_search | A Course in Arithmetic |
| title_full | A Course in Arithmetic by Jean-Pierre Serre |
| title_fullStr | A Course in Arithmetic by Jean-Pierre Serre |
| title_full_unstemmed | A Course in Arithmetic by Jean-Pierre Serre |
| title_short | A Course in Arithmetic |
| title_sort | a course in arithmetic |
| topic | Mathematics Number theory Number Theory Mathematik Analytische Zahlentheorie (DE-588)4001870-2 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd Arithmetik (DE-588)4002919-0 gnd Zahlkörper (DE-588)4067273-6 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Mathematics Number theory Number Theory Mathematik Analytische Zahlentheorie Algebraische Zahlentheorie Arithmetik Zahlkörper Zahlentheorie |
| url | https://doi.org/10.1007/978-1-4684-9884-4 |
| work_keys_str_mv | AT serrejeanpierre acourseinarithmetic |