Class Field Theory

Fretwell, Daniel

ISBN 10: 3640969294 / ISBN 13: 9783640969296

Verlag: Grin Verlag, 2011

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Inhaltsangabe:

Research Paper (postgraduate) from the year 2011 in the subject Mathematics - Number Theory, grade: Postgraduate, University of Sheffield, language: English, abstract: This is the first in a two part series of papers establishing (with proof) the main theorems of global class field theory. We first recap some of the main ideas of algebraic number theory, using these to develop the Artin reciprocity law and the Takagi existence theorem both in terms of ideals and ideles. Finally, we use the Hilbert class field in order to study the well known problem of which prime numbers can be represented in the form x^2 + ny^2 for integers x,y and positive integer n.

Reseña del editor: Research Paper (postgraduate) from the year 2011 in the subject Mathematics - Number Theory, grade: Postgraduate, University of Sheffield, language: English, abstract: This is the first in a two part series of papers establishing (with proof) the main theorems of global class field theory. We first recap some of the main ideas of algebraic number theory, using these to develop the Artin reciprocity law and the Takagi existence theorem both in terms of ideals and ideles. Finally, we use the Hilbert class field in order to study the well known problem of which prime numbers can be represented in the form x^2 + ny^2 for integers x,y and positive integer n.

Bibliografische Details

Titel: Class Field Theory
Verlag: Grin Verlag
Erscheinungsdatum: 2011
Einband: Softcover
Zustand: New