J.L. Lehman

Quadratic Number Theory

An Invitation to Algebraic Methods in the Higher Arithmetic

• Gebundenes Buch

Produktbeschreibung

Offers an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. With its exceptionally clear prose, hundreds of exercises, and historical motivation, this is a textbook for a second undergraduate course in number theory.

Produktdetails

• Dolciani Mathematical Expositions
• Verlag: American Mathematical Society
• Seitenzahl: 394
• Erscheinungstermin: 30. April 2019
• Englisch
• Abmessung: 165mm x 239mm x 23mm
• Gewicht: 656g
• ISBN-13: 9781470447373
• ISBN-10: 1470447371
• Artikelnr.: 56533911

Autorenporträt

J. L. Lehman, University of Mary Washington, Fredericksburg, VA.

Inhaltsangabe

1. Introduction: A brief review of elementary number theory
2. Quadratic domains and ideals: Gaussian integers and sums of two squares
3. Quadratic domains
4. Ideals of quadratic domains
5. Quadratic forms and ideals: Quadratic forms
6. Correspondence between forms and ideals
7. Positive definite quadratic forms: Class groups of negative discriminant
8. Representations by positive definite forms
9. Class groups of quadratic subdomains
10. Indefinite quadratic forms: Continued fractions
11. Class groups of positive discriminant
12. Representations by indefinite forms
13. Quadratic recursive sequences: Properties of recursive sequences
14. Applications of quadratic recursive sequences
15. Concluding remarks
16. List of notation
17. Index