Skip to main content
SpringerLink
Log in

Testing degenerate polynomials

  • Original Paper
  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Two methods to test whether a given polynomial has two distinct roots whose quotient is a root of unity are discussed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berstel J., Mignotte M.: Deux propriétés décidables des suites récurrentes linéaires. Bull. Soc. Math. France 104, 175–184 (1976)

    MathSciNet  MATH  Google Scholar 

  2. Beukers F., Smyth C.J.: Cyclotomic points on curves. In: Bennett, M.A. et al. (eds) Number Theory for the millennium, I (Urbana, Il, 2000), pp. 67–85. A. K. Peters, Natick, Ma (2002)

    Google Scholar 

  3. Boyd D.W.: Irreducible polynomials with many roots of maximal modulus. Acta Arith. 68, 85–88 (1994)

    MathSciNet  MATH  Google Scholar 

  4. Bradford, R.J., Davenport, J.H.: Effective tests for cyclotomic polynomials. In: Symbolic and algebraic computation Roma 1988, Lecture Notes in Computer Science, vol.358, pp. 244–251. Springer, Berlin (1989)

  5. Cerlienco L., Mignotte M., Piras F.: Computing the measure of a polynomial. J. Symb. Comput. 4(1), 21–33 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  6. Choie Y.-J., Lichiardopol N., Moree P., Solé P.: On Robin’s criterion for the Riemann Hypothesis. J. Théorie des Nombres Bordeaux 19(2), 357–377 (2007)

    Article  MATH  Google Scholar 

  7. Cremona J.E.: Unimodular integer circulants. Math. Comput. 77, 1639–1652 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ferguson R.: Irreducible polynomials with many roots of equal modulus. Acta Arith. 78, 221–225 (1997)

    MathSciNet  MATH  Google Scholar 

  9. Hardy G.H., Wright E.M.: An Introduction to the Theory of Numbers. Clarendon Press, Oxford (1979)

    MATH  Google Scholar 

  10. Lang S.: Algebra. Addison-Wesley, Reading, MA (1965)

    MATH  Google Scholar 

  11. Lewis D.J.: Diophantine equations, p–adic methods. In: Le Veque, W.J. (eds) Studies in Number Theory, pp. 25–75. Prentice Hall, New York (1969)

    Google Scholar 

  12. http://www.cecm.sfu.ca/~mjm/Lehmer/

  13. Smyth C.J.: Conjugate algebraic numbers on conics. Acta Arith. 40, 333–346 (1982)

    MathSciNet  MATH  Google Scholar 

  14. Smyth C.J.: Additive and multiplicative relations connecting conjugate algebraic numbers. J. Number Theory 23, 243–254 (1986)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Ismaïla Diouf

    Present address: Département de Mathématiques, Université Cheikh Anta Diop, Dakar, Senegal

Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, P.O. Box 1–764, 014700, Bucharest, Romania

    Mihai Cipu

  2. Département de Mathématiques, Université de Strasbourg, 7, rue René Descartes, 67084, Strasbourg Cedex, France

    Ismaïla Diouf & Maurice Mignotte

Authors
  1. Mihai Cipu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ismaïla Diouf
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maurice Mignotte
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mihai Cipu.

Additional information

During the work to this paper, the first author had a position of Visiting Professor at Université de Strasbourg and was partially supported by Grant CNCSIS 1116/2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cipu, M., Diouf, I. & Mignotte, M. Testing degenerate polynomials. AAECC 22, 289–300 (2011). https://doi.org/10.1007/s00200-011-0150-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00200-011-0150-8

Keywords

Search

Navigation