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Quadratic Forms

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Algebraic Theory of Quadratic Numbers

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Abstract

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.

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Further Reading

  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. Cassels, J.W.S., Frohlich, A. (eds.): Algebraic Number Theory: Proceedings of an Instructional Conference. Thompson Book, Washington, DC (1967)

    Google Scholar 

  3. Cohn, H.: Advanced Number Theory. Dover, New York (1962)

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  4. Conway, J.H.: The Sensual (Quadratic) Form. Mathematical Association of America, Washington (1997)

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  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)

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  6. Harper, M.: \(\mathbb{Z}[\sqrt{14}]\) is Euclidean. Canad. J. Math. 56(1), 55–70 (2004)

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  7. A. Ya. Khinchin.: Continued Fractions. Dover Books on Mathematics Series. Courier Dover Publications, New York (1964)

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  8. Lemmermeyer, F.: Binary quadratic forms: An elementary approach to the arithmetic of elliptic and hyperelliptic curves. Available at http://www.rzuser.uni-heidelberg.de/~hb3/publ/bf.pdf

  9. Marcus, D.A.: Number Fields. Universitext. Springer, New York (1977)

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  10. Mollin, R.A.: Quadratics. In: Discrete Mathematics and Its Applications Series, vol. 2. CRC Press, Boca Raton, FL (1996)

    Google Scholar 

  11. Serre, J.-P.: A course in arithmetic. In: Graduate Texts in Mathematics, Springer, New York (1973)

    Google Scholar 

  12. Zagier, D.B.: Zetafunktionen und quadratische Körper: Eine Einführung in die höhere Zahlentheorie. Hochschultext. Springer, Berlin (1981)

    Google Scholar 

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Trifković, M. (2013). Quadratic Forms. In: Algebraic Theory of Quadratic Numbers. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7717-4_7

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