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Zetafunktionen Und Quadratische Körper

Zetafunktionen Und Quadratische Körper


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About the Book

Das Ziel dieses Buchs ist, die Theorie der binaren quadratischen For- men, die im letzten Jahrhundert in ihren algebraischen Aspekten von GauB und in ihren analytischen Aspekten von Dirichlet entwickelt wurde, darzustellen. Diese Theorie, die frtiher zur normalen Ausbildung in der Mathematik gehorte, wird heute den Studenten oft nur als Beispiel ftir die moderne algebraische Zahlentheorie, analytische Zahlentheorie oder Klassenkorpertheorie prasentiert. Da sie aber eine groBe Schonheit be- sitzt und aUBerdem elementar zuganglich ist, halte ich es ftir zweck- maBiger, sie umgekehrt als Einftihrung in die genannten Gebiete zu be- nutzen, die ja historisch aus ihr hervorgegangen sind. Da das Buch eine Einfuhrung sein solI, sind die voraussetzngen mi- nimal gehalten, und zwar: - aus der Algebra die Grundbegriffe tiber Gruppen und Ringe und der Struktursatz fUr endlich erzeugte abelsche Gru pen; - aus der komplexen Funktionentheorie eigentlich nur die Begriffe "holomorphe Funktion", "meromorphe Funktion", "Residuum" und "ana- lytische Fortsetzung" (der eauchysche Integralsatz wird nie benutzt); - aus der Zahlentheorie etwa der Inhalt einer elementaren einsemestri- gen Vorlesung, insbesondere Kongruenzen, Legendre-Symbol, quadrati- sche Reziprozitat. Das Buch basiert auf Vorlesungen in Bonn (SS 1975) und Harvard (WS 1977) und ist als Vorlaufer eines umfassenderen Buches auf Englisch gedacht. Hanspeter Kraft, David Kramer und Winfried Kohnen, die Teile des Manuskripts gelesen und ausftihrlich kommentiert haben, mochte ich hier herzlich danken; vor allem gilt mein Dank Silke Suter fUr ihre Unterstutzung bei dem ganzen Unternehmen und fUr ihre Hilfe bei sprach- lichen und darstellerischen Schwierigkeiten.


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Product Details
  • ISBN-13: 9783540106036
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 231 mm
  • No of Pages: 144
  • Series Title: Hochschultext
  • Sub Title: Eine Einführung in Die Höhere Zahlentheorie
  • Width: 155 mm
  • ISBN-10: 3540106030
  • Publisher Date: 01 Sep 1981
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 10 mm
  • Weight: 286 gr


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