User:Virginia-American/Sandbox/References
From Wikipedia, the free encyclopedia
Contents |
[edit] See also
- Euler's criterion
- Gauss's lemma
- Zolotarev's lemma
- Law of quadratic reciprocity
- Character sum
- Paley graph
[edit] Notes
[edit] References
The Disquisitiones Arithmeticae has been translated from Gauss's Ciceronian Latin into English and German. The German edition includes all of his papers on number theory: all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes.
- Gauss, Carl Friedrich & Clarke, Arthur A. (translator into English) (1986), Disquisitiones Arithemeticae (Second, corrected edition), New York: Springer, ISBN 0387962549
- Gauss, Carl Friedrich & Maser, H. (translator into German) (1965), Untersuchungen uber hohere Arithmetik (Disquisitiones Arithemeticae & other papers on number theory) (Second edition), New York: Chelsea, ISBN 0-8284-0191-8
- Bach, Eric & Shallit, Jeffrey (1966), Algorithmic Number Theory (Vol I: Efficient Algorithms), Cambridge: The MIT Press, ISBN 0-262-02045-5
- Cohen, Henri (1993), A Course in Computational Algebraic Number Theory, Berlin: Springer, ISBN 3-540-55640-0
- Crandall, Richard & Pomeramce, Carl (2001), Prime Numbers: A Computatinal Perspective, New York: Springer, ISBN 0-387-04777-9
- Davenport, Harold (2000). Multiplicative Number Theory (Third edition). New York: Springer. ISBN 0-387-95097-4.
- Edwards, Harold (1977). Fermat's Last Theorem. New York: Springer. ISBN 0-387-90230-9.
- Michael R. Garey and David S. Johnson (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman. ISBN 0-7167-1045-5. A7.1: AN1, pg.249.}}
- Hardy, G. H. (1999), Ramanujan: Twelve Lectures on Subjects Suggested by his Life and work, Providence RI: AMS / Chelsea, ISBN 978-0821820230
- Hardy, G. H. & Wright, E. M. (1980), An Introduction to the Theory of Numbers (Fifth edition), Oxford: Oxford University Press, ISBN 978-0198531715
- Ireland, Kenneth & Rosen, Michael (1990), A Classical Introduction to Modern Number Theory (Second edition), New York: Springer, ISBN 0-387-97329-X
- Knopfmacher, John (1990), Abstract Analytic Number Theory, New York: Dover, ISBN 0-486-66344-2
- Lemmermeyer, Franz (2000), Reciprocity Laws: from Euler to Eisenstein, Berlin: Springer, ISBN 3-540-66967-4
- Manders, Kenneth L.; Adleman, Leonard (1978). "NP-Complete Decision Problems for Binary Quadratics". Journal of Computer and System Sciences 16 (2): 168–184. doi:.
- Ramanujan (2000), Collected Papers, Providence RI: AMS / Chelsea, ISBN 978-0821820766
- Riesel, Hans (1994), Prime Numbers and Computer Methods for Factorization (second edition), Boston: Birkhäuser, ISBN 0-8176-3743-5
