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Spezielle Funktionen der mathematischen Physik und ihre zahlentheoretischen Analoga by Frantzen, Leonie

Spezielle Funktionen der mathematischen Physik und ihre zahlentheoretischen Analoga

by Leonie Frantzen
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Book cover type: Paperback
  • ISBN13: 9783668710313
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 84
  • Original Price: USD 67.9
  • Language: German
  • Edition: 1. Auflage
  • Item Weight: 123 grams
  • BISAC Subject(s): Vector Analysis

Bachelorarbeit aus dem Jahr 2017 im Fachbereich Mathematik - Analysis, Note: 1,3, Georg-August-Universität Göttingen (Mathematisches Institut), Sprache: Deutsch, Abstract: Die Arbeit schlägt eine Brücke zwischen der Analysis und der Algebra. Wir befassen uns nämlich auf der analytischen Seite mit speziellen Funktionen der mathematischen Physik, auf der algebraischen Seite hingegen mit Charaktersummen über endlichen Körpern. Das Ziel dieser Arbeit besteht darin, die schönen und oftmals erstaunlichen Analogien zwischen bestimmten speziellen Funktionen und ihrem jeweiligen zahlentheoretischen Widerpart aufzudecken. Der erste Teil umfasst drei spezielle Funktionen, nämlich die Gamma-, die Beta- und die Besselfunktion. Dabei befassen wir uns mit analytischer Fortsetzbarkeit, Darstellungen als Integral oder Produkt, Potenzreihenentwicklungen und speziellen Identitäten dieser Funktionen. Im zweiten Teil wenden wir uns der Gau -, der Jacobi- und der Kloostermansumme zu. Dafür entwickeln wir zunächst die Theorie der Charaktere auf dem endlichen Körper. Das Königsresultat der Arbeit ist ein Theorem, das eine Relation zwischen Gamma- und Betafunktion herstellt und ganz analog zwischen Gau - und Jacobisumme funktioniert. Die in dieser Arbeit aufgeführten Behauptungen sind zumeist schon seit längerer Zeit bekannt, aber in der Literatur bisher nicht unbedingt in dieser Form zusammengebracht worden. Die Absicht der Verfasserin war es, die relevanten Aussagen auszuwählen und sie auf eine Art zu beweisen, dass ein Bachelorabsolvent sie nachvollziehen kann.

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