Skip to main content
Log in

Uniformly distributed sequences in computer algebra or how to construct program generators of random numbers

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. V. S. Anashin, “Uniformly distributed sequences ofp-adic integers,”Mat. Zametki,55, No. 2, 3–46 (1994).

    MATH  MathSciNet  Google Scholar 

  2. V. S. Anashin, “Solvable groups with operators and commutative rings possessing transitive polynomials,”Algebra Logika,21, No. 6, 627–646 (1982).

    MathSciNet  Google Scholar 

  3. V. S. Anashin, “Mixed identities and mixed varieties of groups,”Mat. Sb.,129, No. 2, 163–174 (1986).

    MATH  MathSciNet  Google Scholar 

  4. V. S. Anashin and M. V. Larin, “On the interpolation onA 5” [in Russian], In:Abstract of Reports on Group Theory. The 8th All-Union Symposium, Sums, May 24–27, 1982. (1982), pp. 6–7.

  5. E. F. Brickell and E. M. Odlizko, “Cryptoanalysis: review of the latest results,”IEEE,76, No. 5, 75–93 (1988).

    Google Scholar 

  6. L. Kuipers and G. Niederreiter,Uniform Distribution of Sequences, John Wiley and Sons, New York-London-Toronto (1974).

    Google Scholar 

  7. M. Kline,Mathematics. The Loss of Certainty, Oxford Univ. Press, Oxford (1980).

    Google Scholar 

  8. D. Knuth,The Art of Computer Programming. 2. Seminumerical Algorithms, Addison-Wesley, Reading, Massachusetts (1969).

    Google Scholar 

  9. N. Koblitz,p-Adic Numbers, p-Adic Analysis and Zeta-Functions, Springer, Heidelberg (1977).

    Google Scholar 

  10. R. Crowell and R. Fox,Introduction to the Knot Theory, Ginu and Co., Boston (1963).

    Google Scholar 

  11. A. G. Kurosh,General Algebra (lectures of 1969–1970) [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  12. H. NeumannVarieties of Groups, Springer-Verlag, Berlin-Heidelberg-New York (1967).

    Google Scholar 

  13. V. S. Anashin, “Uniformly distributed sequences overp-adic integers,” In:Number Theoretic and Algebraic Methods in Computer Science, Proc. of Intern. Conf., Moscow, June–July, 1993, World Scientific (1995), pp. 1–18.

  14. V. S. Anashin,Uniformly Distributed Sequences over p-Adic Integers, Russian State University for the Humanities, Moscow (1993).

    Google Scholar 

  15. J. Eichenauer-Herrmann, “Inversive congruential pseudorandom numbers: a tutorial,”Intern. Statist. Rev.,60, 167–176 (1992).

    MATH  Google Scholar 

  16. R. R. Hall, “On pseudo-polynomials,”Mathematika (Gr. Brit.),18, No. 1, 71–77 (1971).

    MATH  MathSciNet  Google Scholar 

  17. D. Jonah and B. M. Schreiber, “Transitive affine transformations of discrete groups,”Pacif. J. Math.,58, No. 2, 483–509 (1975).

    MathSciNet  Google Scholar 

  18. H. K. Kaiser and W. Nöbauer, “Permutation polynomials in several variables over residue class rings,”J. Austral. Math. Soc. A43, No. 2, 171–175 (1987).

    Google Scholar 

  19. H. Lausch, “Interpolation on the alternating groupA 5,” in:Contrib. Gen. Algebra. Proc. Klangenfurt Conf. 1978, J. Heyn, Klangenfurt (1979), pp. 187–192.

    Google Scholar 

  20. H. Lausch, “Zur Theorie der Polynompermutationen über endlichen Gruppen,”Arch. Math.,19, No. 3, 284–288 (1968).

    MATH  MathSciNet  Google Scholar 

  21. H. Lausch and W. Nöbauer,Algebra of Polynomials North-Holland, Amsterdam-London (1973).

    Google Scholar 

  22. K. Mahler,p-Adic Numbers and Their Functions, 2nd ed. Cambridge Univ. Press (1981).

  23. B. R. McDonald,Finite Rings with Identity, Marcel Dekker, New York (1974).

    Google Scholar 

  24. H. Niederreiter, “Nonlinear methods for pseudorandom number and vector generation,”Lect. Notes Econ. Math. Syst., 145–153 (1992).

  25. H. Niederreiter,Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, Ch. 8 (1992).

    Google Scholar 

Download references

Authors

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 31, Computing Mathematics and Cybernetics-2, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anashin, V.S. Uniformly distributed sequences in computer algebra or how to construct program generators of random numbers. J Math Sci 89, 1355–1390 (1998). https://doi.org/10.1007/BF02355442

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02355442

Keywords

Navigation