Skip to main content
Log in

Irreducible polynomials over a finite field

  • Published:
Siberian Mathematical Journal 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.

Literature Cited

  1. S. I. Gel'fand, “Irreducible polynomials over a finite field,” Usp. Mat. Nauk,24, No. 4, 193–194 (1969).

    Google Scholar 

  2. G. L. Watson, “Sums of eight values of a cubic polynomial,” J. London Math. Soc.,27, No. 2, 217–224 (1952).

    Google Scholar 

  3. L. Garlitz, “A theorem of Dickson on irreducible polynomials,” Proc. Am. Math. Soc.,3, No. 5, 693–700 (1952).

    Google Scholar 

  4. D. R. Hayes, “The distribution of irreducibles in GF[q, x],” Trans. Am. Math. Soc.,117, 101–127 (1965).

    Google Scholar 

  5. S. D. Cohen, “Uniform distribution of polynomials over finite fields,” J. London Math. Soc. Ser. 2,6, No. 1, 93–102 (1972).

    Google Scholar 

  6. S. A. Stepanov, “On the number of irreducible in Fq[x] polynomials of a special form,” Usp. Mat. Nauk,40, No. 4, 199–200 (1985).

    Google Scholar 

  7. S. Chowla, “A note on the construction of finite Galois fields GF(pn),” J. Math. Anal. Appl.,15, 53–54 (1966).

    Google Scholar 

  8. R. Ree, “Proof of a conjecture of S. Chowla,” J. Number Theory,3, No. 2, 210–212 (1971).

    Google Scholar 

  9. B. J. Birch and H. P. F. Swinnerton-Dyer, “Note on a problem of Chowla,” Act. Arithm.,5, 417–423 (1959).

    Google Scholar 

  10. P. A. Leonard, “On constructing quartic extensions of GF(p),” Norske Vid. Selsk. Forh. (Trondheim),40, 96–97 (1967).

    Google Scholar 

  11. K. S. Williams, “On two conjectures of Chowla,” Can. Math. Bull.,12, No. 5, 545–565 (1969).

    Google Scholar 

  12. S. Lang, Algebra, Addison-Wesley, MA (1965).

    Google Scholar 

  13. R. Lidl and H. Niederreiter, Finite Fields [Russian translation], Vol. 1, Mir, Moscow (1988).

    Google Scholar 

Download references

Authors

Additional information

Dedicated to the memory of A. I. Mal'tsev.

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 6, pp. 98–109, November–December, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuz'min, E.N. Irreducible polynomials over a finite field. Sib Math J 30, 915–925 (1989). https://doi.org/10.1007/BF00970914

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970914

Keywords

Navigation