Copied Analytische Funktionen in der Zahlentheorie
Analytische Funktionen in der Zahlentheorie
Im Mittelpunkt des Buches steht die Behandlung von Funktionalgleichungen analytischer Funktionen, die fr die Anwendungen in der Zahlentheorie von Interesse sind. Ausgehend vom Gedankenkreis des quadratischen Reziprozittsgesetzes werden die analytischen Grundlagen durch die Jacobischen Thetafunktionen und die Dedekindsche Etafunktion gelegt und ihre Beziehungen zu den Gauschen und Dedekindschen Summen errtert. Anschlieend werden Verallgemeinerungen dieser Funktionen bezglich hherer arithmetischer Probleme besprochen. Schlielich werden analytische Funktionen ber konvexen Krpern betrachtet und Abschtzungen von Gitterpunktanzahlen in konvexen Krpern vorgenommen.
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