Quadratic Number Theory

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

• Introduction: A brief review of elementary number theoryQuadratic domains and ideals: Gaussian integers and sums of two squaresQuadratic domainsIdeals of quadratic domainsQuadratic forms and ideals: Quadratic formsCorrespondence between forms and idealsPositive definite quadratic forms: Class groups of negative discriminantRepresentations by positive definite formsClass groups of quadratic subdomainsIndefinite quadratic forms: Continued fractionsClass groups of positive discriminantRepresentations by indefinite formsQuadratic recursive sequences: Properties of recursive sequencesApplications of quadratic recursive sequencesConcluding remarksList of notationIndex