ENGLISH

Quadratic Number Fields

By Franz Lemmermeyer

Book information

Publisher
Springer Nature Switzerland AG
Year
2021
ISBN
9783030786519, 9783030786526
Language
english
Format
EPUB
Filesize
17 MB (18241482 bytes)
Series
Springer Undergraduate Mathematics
Edition
1
Pages
343\0
Topic
Mathematics Algebra
Time added
2025-02-01 20:07:22

Description

This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level.Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study.Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.

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