Basis reduction and evidence for transcendence of certain numbers

  • Ravi Kannan
  • Lyle A. McGeoch
Session 4 Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 241)


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6 References

  1. Hermite, Ch. Sur la fonction exponentielle. Oeuvres III (1873), 150–181.Google Scholar
  2. Kannan, R., A. Lenstra and L. Lovász. Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers. In Proceedings of the 16-th ACM Symposium on Theory of Computing (1984, Washington), 191–200.Google Scholar
  3. Kannan, R., L. McGeoch, and L. Tadj. Computational results on the subset sum problem. In preparation (1986).Google Scholar
  4. Lang, S.Algebra. Addison-Wesley, Reading, Massachusetts, 1965.Google Scholar
  5. Lang, S.Introduction to Transcendental Numbers. Addison-Wesley Series in Mathematics, 1966.Google Scholar
  6. Lenstra, A., H. Lenstra and L. Lovász Factoring polynomials with rational coefficients. Mathematische Annalen 261 (1982), 513–534.Google Scholar
  7. Lindenmann, F. Über die Zahl π. Math. Annalen 20 (1882), 213–225.Google Scholar
  8. Marcus, D.Number Fields. Springer Verlag, 1945.Google Scholar
  9. Schönhage, A. Factorization of univariate integer polynomials by Diophantine approximation and an improved basis reduction algorithm. In 11-th International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science 172, Springer-Verlag, 1984, 436–447.Google Scholar
  10. Stewart, I., and D. Tall. Algebraic Number Theory. Chapman and Hall, London, 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Ravi Kannan
    • 1
  • Lyle A. McGeoch
    • 1
  1. 1.Computer Science DepartmentCarnegie-Mellon UniversityPittsburghUSA

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