Class Field Theory

ISBN-13: 9783640969296 / Angielski / Miękka / 2011 / 24 str.

Daniel Fretwell

Opis

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 DEGREES2 + ny DEGREES2 for integers x, y and posi