Algebraic Theory of Quadratic Numbers

This document was uploaded by one of our users. The uploader already confirmed that they had the permission to publish it. If you are author/publisher or own the copyright of this documents, please report to us by using this DMCA report form.

Simply click on the Download Book button.

Yes, Book downloads on Ebookily are 100% Free.

Sometimes the book is free on Amazon As well, so go ahead and hit "Search on Amazon"

By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes.

The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic familiarity with ring theory.

Author(s): Mak Trifković (auth.)
Series: Universitext
Edition: 1
Publisher: Springer-Verlag New York
Year: 2013

Language: English
Pages: 197
Tags: Number Theory; Algebra

Front Matter....Pages i-xi
Examples....Pages 1-25
A Crash Course in Ring Theory....Pages 27-44
Lattices....Pages 45-59
Arithmetic in $$\mathbb{Q}[\sqrt{D}]$$ ....Pages 61-86
The Ideal Class Group and the Geometry of Numbers....Pages 87-105
Continued Fractions....Pages 107-130
Quadratic Forms....Pages 131-184
Back Matter....Pages 185-197