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  • 1
    Book
    Book
    A course in arithmetic (1973)
    New York : Springer
    Details
    UID:
    gbv_02034161X
    Format: VIII, 115 Seiten , graph. Darstellungen , 25 cm
    ISBN: 0387900403 , 3540900403 , 0387900411 , 3540900411
    Series Statement: Graduate texts in mathematics 7
    Uniform Title: Cours d'arithmétique 〈engl.〉
    Note: Corrected fifth printing"--T.p. verso , Literaturverz. S. 112 - 113
    Additional Edition: Erscheint auch als Online-Ausgabe Serre, Jean-Pierre, 1926 - A Course in Arithmetic New York, NY : Springer, 1973 ISBN 9781468498844
    Language: English
    Subjects: Mathematics
    RVK:
    SK 180
    Keywords: Algebraische Zahlentheorie ; Analytische Zahlentheorie
    URL: Inhaltsverzeichnis
    URL: Cover
    URL: http://www.loc.gov/catdir/enhancements/fy0817/70190089-t.html
    Author information: Serre, Jean-Pierre 1926-
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  • 2
    Online Resource
    Online Resource
    A Course in Arithmetic (1973)
    New York, NY :Springer New York :
    Details
    UID:
    almahu_9947363082202882
    Format: IX, 118 p. , online resource.
    ISBN: 9781468498844
    Series Statement: Graduate Texts in Mathematics, 7
    Content: 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.
    Note: 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.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780387900414
    Language: English
    DOI: 10.1007/978-1-4684-9884-4
    URL: http://dx.doi.org/10.1007/978-1-4684-9884-4
    URL: Volltext
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
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    HU Berlin
    BTU Cottbus
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