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Cover: 9780387900407 | A Course in Arithmetic | J-P. Serre | Buch | ix | Englisch | 1978
Bild: 9780387900407 | A Course in Arithmetic | J-P. Serre | Buch | ix | Englisch | 1978
Cover: 9780387900407 | A Course in Arithmetic | J-P. Serre | Buch | ix | Englisch | 1978
Bild: 9780387900407 | A Course in Arithmetic | J-P. Serre | Buch | ix | Englisch | 1978
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A Course in Arithmetic
Buch von J-P. Serre
Sprache: Englisch

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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 atthe 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.
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 atthe 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.
Inhaltsverzeichnis
I-Algebraic Methods.- I-Finite fields.- II - p-adic fields.- III-Hilbert symbol.- IV-Quadratic forms over Qp and over Q.- V-Integral quadratic forms with discriminant ± 1.- II-Analytic Methods.- VI-The theorem on arithmetic progressions.- VII-Modular forms.- Index of Definitions.- Index of Notations.
Details
Erscheinungsjahr: 1978
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: ix
119 S.
ISBN-13: 9780387900407
ISBN-10: 0387900403
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Serre, J-P.
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 241 x 160 x 13 mm
Von/Mit: J-P. Serre
Erscheinungsdatum: 29.11.1978
Gewicht: 0,371 kg
Artikel-ID: 101267537
Inhaltsverzeichnis
I-Algebraic Methods.- I-Finite fields.- II - p-adic fields.- III-Hilbert symbol.- IV-Quadratic forms over Qp and over Q.- V-Integral quadratic forms with discriminant ± 1.- II-Analytic Methods.- VI-The theorem on arithmetic progressions.- VII-Modular forms.- Index of Definitions.- Index of Notations.
Details
Erscheinungsjahr: 1978
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: ix
119 S.
ISBN-13: 9780387900407
ISBN-10: 0387900403
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Serre, J-P.
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 241 x 160 x 13 mm
Von/Mit: J-P. Serre
Erscheinungsdatum: 29.11.1978
Gewicht: 0,371 kg
Artikel-ID: 101267537
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