Quadratic Number Fields

Franz Lemmermeyer

ISBN 10: 303078651X / ISBN 13: 9783030786519

Editore: Springer International Publishing, Springer International Publishing Sep 2021, 2021

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Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 356 pp. Englisch.

Codice articolo 9783030786519

Dati bibliografici

• Titolo: Quadratic Number Fields
• Editore: Springer International Publishing, Springer International Publishing Sep 2021
• Data di pubblicazione: 2021
• Lingua: Inglese
• ISBN 10: 303078651X
• ISBN 13: 9783030786519
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 20 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 20 millimetri di profondità
• Peso: 540 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

Franz Lemmermeyer has worked in algebraic number theory and has published several books on the history of number theory, in particular on reciprocity laws.