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Year 2020, , 98 - 109, 14.07.2020
https://doi.org/10.24330/ieja.768184

Abstract

References

  • J.-P. Borel, Suites de longueur minimale associees a un ensemble normal donne, Israel J. Math., 64 (1988), 229-250.
  • J.-P. Borel, Polynomes a coeffcients positifs multiples d'un polynome donne, in Cinquante ans de polynomes (Paris, 1988), Lecture Notes in Math., Springer, Berlin, 1415 (1990), 97-115.
  • H. Brunotte, A remark on roots of polynomials with positive coeffcients, Manuscripta Math., 129 (2009), 523-524.
  • H. Brunotte, On real polynomials without nonnegative roots, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 26 (2010), 31-34.
  • H. Brunotte, On expanding real polynomials with a given factor, Publ. Math. Debrecen, 83 (2013), 161-178.
  • H. Brunotte, Polynomials with nonnegative coeffcients and a given factor, Period. Math. Hungar., 66 (2013), 61-72.
  • H. Brunotte, On some classes of polynomials with nonnegative coeffcients and a given factor, Period. Math. Hungar., 67 (2013), 15-32.
  • H. Brunotte, On canonical representatives of small integers, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 30 (2014), 1-15.
  • I. Dancs, Remarks on a paper of P. Turan, Ann. Univ. Sci. Budapest. Eotvos Sect. Math., 7 (1964), 133-141.
  • V. De Angelis, Asymptotic expansions and positivity of coeffcients for large powers of analytic functions, Int. J. Math. Math. Sci., (2003), 1003-1025.
  • H. G. Diamond and M. Essen, Functions with non-negative convolutions, J. Math. Anal. Appl., 63 (1978), 463-489.
  • A. Dubickas, On roots of polynomials with positive coeffcients, Manuscripta Math., 123 (2007), 353-356.
  • P. Kirschenhofer and J. M. Thuswaldner, Shift radix systems-a survey, in Numeration and substitution 2012, RIMS Kokyuroku Bessatsu, B46, Res. Inst. Math. Sci. (RIMS), Kyoto, (2014), 1-59.
  • G. Kuba, Several types of algebraic numbers on the unit circle, Arch. Math. (Basel), 85 (2005), 70-78.
  • V. Laohakosol and S. Tadee, Algebraic numbers satisfying polynomials with positive rational coeffcients, J. Numbers, (2014), 1-8.
  • E. Meissner, Uber positive Darstellungen von Polynomen, Math. Ann., 70 (1911), 223-235.
  • T. S. Motzkin and E. G. Straus, Divisors of polynomials and power series with positive coeffcients, Paci c J. Math., 29 (1969), 641-652.
  • V. Ponomarenko, Arithmetic of semigroup semirings, Ukrainian Math. J., 67 (2015), 243-266. Reprint of Ukrain. Mat. Zh. 67(2) (2015), 213-229.
  • I. SageMath, CoCalc Collaborative Computation Online, 2017. https://cocalc.com/.
  • C. Tan and W.-K. To, Characterization of polynomials whose large powers have all positive coeffcients, Proc. Amer. Math. Soc., 146 (2018), 589-600.
  • T. Zaimi, On roots of polynomials with positive coeffcients, Publ. Inst. Math. (Beograd) (N.S.), 89(103) (2011), 89-93.

INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS

Year 2020, , 98 - 109, 14.07.2020
https://doi.org/10.24330/ieja.768184

Abstract

For a given real polynomial $f$ without nonnegative roots we study monic integer polynomials $g$ such that the product $g f$ has positive (nonnegative, respectively) coefficients. We show that monic integer polynomials~$g$ with these properties can effectively be computed, and we give lower and upper bounds for their degrees. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

References

  • J.-P. Borel, Suites de longueur minimale associees a un ensemble normal donne, Israel J. Math., 64 (1988), 229-250.
  • J.-P. Borel, Polynomes a coeffcients positifs multiples d'un polynome donne, in Cinquante ans de polynomes (Paris, 1988), Lecture Notes in Math., Springer, Berlin, 1415 (1990), 97-115.
  • H. Brunotte, A remark on roots of polynomials with positive coeffcients, Manuscripta Math., 129 (2009), 523-524.
  • H. Brunotte, On real polynomials without nonnegative roots, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 26 (2010), 31-34.
  • H. Brunotte, On expanding real polynomials with a given factor, Publ. Math. Debrecen, 83 (2013), 161-178.
  • H. Brunotte, Polynomials with nonnegative coeffcients and a given factor, Period. Math. Hungar., 66 (2013), 61-72.
  • H. Brunotte, On some classes of polynomials with nonnegative coeffcients and a given factor, Period. Math. Hungar., 67 (2013), 15-32.
  • H. Brunotte, On canonical representatives of small integers, Acta Math. Acad. Paedagog. Nyhazi. (N.S.), 30 (2014), 1-15.
  • I. Dancs, Remarks on a paper of P. Turan, Ann. Univ. Sci. Budapest. Eotvos Sect. Math., 7 (1964), 133-141.
  • V. De Angelis, Asymptotic expansions and positivity of coeffcients for large powers of analytic functions, Int. J. Math. Math. Sci., (2003), 1003-1025.
  • H. G. Diamond and M. Essen, Functions with non-negative convolutions, J. Math. Anal. Appl., 63 (1978), 463-489.
  • A. Dubickas, On roots of polynomials with positive coeffcients, Manuscripta Math., 123 (2007), 353-356.
  • P. Kirschenhofer and J. M. Thuswaldner, Shift radix systems-a survey, in Numeration and substitution 2012, RIMS Kokyuroku Bessatsu, B46, Res. Inst. Math. Sci. (RIMS), Kyoto, (2014), 1-59.
  • G. Kuba, Several types of algebraic numbers on the unit circle, Arch. Math. (Basel), 85 (2005), 70-78.
  • V. Laohakosol and S. Tadee, Algebraic numbers satisfying polynomials with positive rational coeffcients, J. Numbers, (2014), 1-8.
  • E. Meissner, Uber positive Darstellungen von Polynomen, Math. Ann., 70 (1911), 223-235.
  • T. S. Motzkin and E. G. Straus, Divisors of polynomials and power series with positive coeffcients, Paci c J. Math., 29 (1969), 641-652.
  • V. Ponomarenko, Arithmetic of semigroup semirings, Ukrainian Math. J., 67 (2015), 243-266. Reprint of Ukrain. Mat. Zh. 67(2) (2015), 213-229.
  • I. SageMath, CoCalc Collaborative Computation Online, 2017. https://cocalc.com/.
  • C. Tan and W.-K. To, Characterization of polynomials whose large powers have all positive coeffcients, Proc. Amer. Math. Soc., 146 (2018), 589-600.
  • T. Zaimi, On roots of polynomials with positive coeffcients, Publ. Inst. Math. (Beograd) (N.S.), 89(103) (2011), 89-93.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Horst Brunotte This is me

Publication Date July 14, 2020
Published in Issue Year 2020

Cite

APA Brunotte, H. (2020). INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS. International Electronic Journal of Algebra, 28(28), 98-109. https://doi.org/10.24330/ieja.768184
AMA Brunotte H. INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS. IEJA. July 2020;28(28):98-109. doi:10.24330/ieja.768184
Chicago Brunotte, Horst. “INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS”. International Electronic Journal of Algebra 28, no. 28 (July 2020): 98-109. https://doi.org/10.24330/ieja.768184.
EndNote Brunotte H (July 1, 2020) INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS. International Electronic Journal of Algebra 28 28 98–109.
IEEE H. Brunotte, “INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS”, IEJA, vol. 28, no. 28, pp. 98–109, 2020, doi: 10.24330/ieja.768184.
ISNAD Brunotte, Horst. “INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS”. International Electronic Journal of Algebra 28/28 (July 2020), 98-109. https://doi.org/10.24330/ieja.768184.
JAMA Brunotte H. INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS. IEJA. 2020;28:98–109.
MLA Brunotte, Horst. “INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS”. International Electronic Journal of Algebra, vol. 28, no. 28, 2020, pp. 98-109, doi:10.24330/ieja.768184.
Vancouver Brunotte H. INTEGER MULTIPLIERS OF REAL POLYNOMIALS WITHOUT NONNEGATIVE ROOTS. IEJA. 2020;28(28):98-109.