Computational number theory

Summary

In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry.[1] Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program.[1][2][3]

Software packages

Further reading

  • Eric Bach; Jeffrey Shallit (1996). Algorithmic Number Theory, Volume 1: Efficient Algorithms. MIT Press. ISBN 0-262-02405-5.
  • Hans Riesel (1994). Prime Numbers and Computer Methods for Factorization. Progress in Mathematics. 126 (second ed.). Birkhäuser. ISBN 0-8176-3743-5. Zbl 0821.11001.

References

  1. ^ a b Carl Pomerance (2009), Timothy Gowers (ed.), "Computational Number Theory" (PDF), The Princeton Companion to Mathematics, Princeton University Press
  2. ^ Eric Bach; Jeffrey Shallit (1996). Algorithmic Number Theory, Volume 1: Efficient Algorithms. MIT Press. ISBN 0-262-02405-5.
  3. ^ Henri Cohen (1993). A Course In Computational Algebraic Number Theory. Graduate Texts in Mathematics. 138. Springer-Verlag. doi:10.1007/978-3-662-02945-9. ISBN 0-387-55640-0.

External links

  • Media related to Computational number theory at Wikimedia Commons