Quadratic Forms

  • Mak Trifković
Part of the Universitext book series (UTX)


In this final chapter we go back to the late-eighteenth-century roots of algebraic number theory. Its fathers, Lagrange, Legendre, and Gauss, had none of the algebraic machinery we have used.

Further Reading

  1. 1.
    Bhargava, M.: Higher composition laws. I. A new view on Gauss composition, and quadratic generalizations. Ann. Math. (2) 159(1), 217–250 (2004)Google Scholar
  2. 2.
    Cassels, J.W.S., Frohlich, A. (eds.): Algebraic Number Theory: Proceedings of an Instructional Conference. Thompson Book, Washington, DC (1967)Google Scholar
  3. 3.
    Cohn, H.: Advanced Number Theory. Dover, New York (1962)Google Scholar
  4. 4.
    Conway, J.H.: The Sensual (Quadratic) Form. Mathematical Association of America, Washington (1997)Google Scholar
  5. 5.
    Cox, D.: Primes of the form x 2 + ny 2: fermat, class field theory, and complex multiplication. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts Monographs and Textbooks in Pure and Applied Mathematics, vol. 34. Wiley, New York (1997)Google Scholar
  6. 6.
    Harper, M.: \(\mathbb{Z}[\sqrt{14}]\) is Euclidean. Canad. J. Math. 56(1), 55–70 (2004)Google Scholar
  7. 7.
    A. Ya. Khinchin.: Continued Fractions. Dover Books on Mathematics Series. Courier Dover Publications, New York (1964)Google Scholar
  8. 8.
    Lemmermeyer, F.: Binary quadratic forms: An elementary approach to the arithmetic of elliptic and hyperelliptic curves. Available at
  9. 9.
    Marcus, D.A.: Number Fields. Universitext. Springer, New York (1977)Google Scholar
  10. 10.
    Mollin, R.A.: Quadratics. In: Discrete Mathematics and Its Applications Series, vol. 2. CRC Press, Boca Raton, FL (1996)Google Scholar
  11. 11.
    Serre, J.-P.: A course in arithmetic. In: Graduate Texts in Mathematics, Springer, New York (1973)Google Scholar
  12. 12.
    Zagier, D.B.: Zetafunktionen und quadratische Körper: Eine Einführung in die höhere Zahlentheorie. Hochschultext. Springer, Berlin (1981)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Mak Trifković
    • 1
  1. 1.Department of Math and StatisticsUniversity of VictoriaVictoriaCanada

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