Description

Book Synopsis
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.

Table of Contents
  • Introduction: A brief review of elementary number theory
  • Quadratic domains and ideals: Gaussian integers and sums of two squares
  • Quadratic domains
  • Ideals of quadratic domains
  • Quadratic forms and ideals: Quadratic forms
  • Correspondence between forms and ideals
  • Positive definite quadratic forms: Class groups of negative discriminant
  • Representations by positive definite forms
  • Class groups of quadratic subdomains
  • Indefinite quadratic forms: Continued fractions
  • Class groups of positive discriminant
  • Representations by indefinite forms
  • Quadratic recursive sequences: Properties of recursive sequences
  • Applications of quadratic recursive sequences
  • Concluding remarks
  • List of notation
  • Index

    Quadratic Number Theory

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      A Hardback by J.L. Lehman

      3 in stock

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        Publisher: American Mathematical Society
        Publication Date: Publication Date: 30/04/2019
        ISBN13: 9781470447373, 978-1470447373
        ISBN10: 1470447371

        Description

        Book Synopsis
        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.

        Table of Contents
        • Introduction: A brief review of elementary number theory
        • Quadratic domains and ideals: Gaussian integers and sums of two squares
        • Quadratic domains
        • Ideals of quadratic domains
        • Quadratic forms and ideals: Quadratic forms
        • Correspondence between forms and ideals
        • Positive definite quadratic forms: Class groups of negative discriminant
        • Representations by positive definite forms
        • Class groups of quadratic subdomains
        • Indefinite quadratic forms: Continued fractions
        • Class groups of positive discriminant
        • Representations by indefinite forms
        • Quadratic recursive sequences: Properties of recursive sequences
        • Applications of quadratic recursive sequences
        • Concluding remarks
        • List of notation
        • Index

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