Quadratic irrationals. An introduction to classical number theory

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"This work focuses on the number theory of quadratic irrationalities in various forms, including continued fractions, orders in quadratic number fields, and binary quadratic forms. It presents classical results obtained by the famous number theorists Gauss, Legendre, Lagrange, and Dirichlet. Collecting information previously scattered in the literature, the book covers the classical theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational"-- Read more... Abstract: "This work focuses on the number theory of quadratic irrationalities in various forms, including continued fractions, orders in quadratic number fields, and binary quadratic forms. It presents classical results obtained by the famous number theorists Gauss, Legendre, Lagrange, and Dirichlet. Collecting information previously scattered in the literature, the book covers the classical theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational" Content: Ch. 1. Quadratic irrationals -- ch. 2. Continued fractions -- ch. 3. Quadratic residues and Gauss sums -- ch. 4. L-series and Dirichlet's prime number theorem -- ch. 5. Quadratic orders -- ch. 6. Binary quadratic forms -- ch. 7. Cubic and biquadratic residues -- ch. 8. Class groups.