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Original Articles

Counting and Testing Dominant Polynomials

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References

  • [Akiyama and Pethő 14a] S. Akiyama and A. Pethő. “The Distribution of Polynomials with Bounded Roots I: Polynomials with Real Coefficients.” J. Math. Soc. Japan 66 (2014), 927–949.
  • [Akiyama and Pethő 14b] S. Akiyama and A. Pethő. “The Distribution of Polynomials with Bounded Roots II. Polynomials with Integer Coefficients.” Uniform Distribution Theory 9 (2014), 5–19.
  • [Akiyama et al. 08] S. Akiyama, H. Brunotte, A. Pethő, and J. M. Thuswaldner. “Generalized Radix Representations and Dynamical Systems IV.” Indag. Math. (N. S.) 19 (2008), 333–348.
  • [Bistritz 84] Y. Bistritz. “Zero Location with Respect to the Unit Circle of Discrete-Time Linear System Polynomials.” Proceedings of the IEEE 72 (1984), 1131–1142.
  • [Bistritz 86] Y. Bistritz. “A Circular Stability Test for General Polynomials.” Systems and Control Letters 7 (1986), 89–97.
  • [Bistritz 02] Y. Bistritz. “Zero Location of Polynomials with Respect to the Unit Circle Unhampered by Nonessential Singularities.” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49 (2002), 305–314.
  • [Boyd 94] D. W. Boyd. “Irreducible polynomials with many roots of maximal modulus.” Acta Arith. 68 (1994), 85–88.
  • [Budarina and Göetze] N. V. Budarina and F. Göetze. “Distance between Conjugate Algebraic Numbers in Clusters.” Math. Notes 94 (2013), 816–819.
  • [Bugeaud and Dujella 11] Y. Bugeaud and A. Dujella. “Root Separation for Irreducible Integer Polynomials.” Bull. London Math. Soc. 43 (2011), 1239–1244.
  • [Bugeaud and Dujella 14] Y. Bugeaud and A. Dujella. “Root Separation for Reducible Integer Polynomials.” Acta Arith. 162 (2014), 393–403.
  • [Bugeaud and Mignotte 10] Y. Bugeaud and M. Mignotte. “Polynomial Root Separation.” Int. J. Number Theory 6 (2010), 587–602.
  • [Bugeaud and Mignotte 11] Y. Bugeaud and M. Mignotte. “On the Distance between Roots of Integer Polynomials.” Proc. Edinb. Math. Soc. 47 (2004), 553–556.
  • [Cauchy 29] A. L. Cauchy. Exercises de Mathématique, 4ème année. De Bure Frères, Paris, 1829.
  • [Corvaja and Zannier 98] P. Corvaja and U. Zannier. “Diophantine Equations with Power Sums and Universal Hilbert Sets.” Indag. Math. 9 (1998), 317–332.
  • [Corvaja and Zannier 02] P. Corvaja and U. Zannier. “Finiteness of Integral Values for the Ratio of Two Linear Recurrences.” Invent. Math. 149 (2002), 431–451.
  • [Dubickas 13] A. Dubickas. “Polynomial Root Separation in Terms of the Remak Height.” Turk. J. Math. 37 (2013), 747–761.
  • [Dubickas and Sha 15] A. Dubickas and M. Sha. “Counting Degenerate Polynomials of Fixed Degree and Bounded Height.” http://arxiv.org/abs/1402.5430, 2015.
  • [Edelman and Kostlan 95] A. Edelman and E. Kostlan. “How Many Zeros of a Random Polynomial Are Real?” Bull. Amer. Math. Soc. 32 (1995), 1–37.
  • [Evertse 04] J.-H. Evertse. “Distances between the Conjugates of an Algebraic Number.” Publ. Math. Debrecen 65 (2004), 323–340.
  • [Fel’dman 81] N. I. Fel’dman. Approximations of Algebraic Numbers ( in Russian). Moskov. Gos. Univ., Moscow, 1981.
  • [Ferguson 97] R. Ferguson. “Irreducible Polynomials with Many Roots of Equal Modulus.” Acta Arith. 78 (1997), 221–225.
  • [Kuba 09] G. Kuba. “On the Distribution of Reducible Polynomials.” Math. Slovaca 59 (2009), 349–356.
  • [Mahler 64] K. Mahler. “An Inequality for the Discriminant of a Polynomial.” Michigan Math. J. 11 (1964), 257–262.
  • [Mehlhorn and Sagraloff 11] K. Mehlhorn and M. Sagraloff. “A Deterministic Algorithm for Isolating Real Roots of a Real Polynomial.” J. Symb. Computat. 46 (2011), 70–90.
  • [Mignotte and Ştefănescu 99] M. Mignotte and D. Ştefănescu. Polynomials: An Algorithmic Approach. Springer, 1999.
  • [Mishra 93] B. Mishra. Algorithmic Algebra. Springer, 1993.
  • [Prasolov 10] V. V. Prasolov. Polynomials, Algorithms and Computation in Mathematics 11. Springer, 2010.
  • [Sagraloff 14] M. Sagraloff. “On the Complexity of the Descartes Method When Using Approximate Arithmetic.” J. Symb. Comput. 65 (2014), 79–110.
  • [Van der Poorten 88] A. J. van der Poorten. “Solution de la conjecture de Pisot sur le quotient de Hadamard de deux fractions rationnelles.” C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), 97–102.
  • [Waldschmidt 00] M. Waldschmidt. Diophantine Approximation on Linear Algebraic Groups. Transcendence Properties of the Exponential Function in Several Variables, Grundlehren der Mathematischen Wissenschaften 326. Springer, 2000.

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