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Around some extensions of Casas-Alvero conjecture for non-polynomial functions

    1. [1] Departament de Matemàtiques, Universitat Autònoma de Barcelona Barcelona, Spain
  • Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 35, Nº 2, 2020, págs. 221-228
  • Idioma: inglés
  • DOI: 10.17398/2605-5686.35.2.221
  • Enlaces
  • Resumen
    • We show that two natural extensions of the real Casas-Alvero conjecture in the non-polynomial setting do not hold.

  • Referencias bibliográficas
    • [1] E. Casas-Alvero, Higher order polar germs, J. Algebra 240 (2001), 326 – 337.
    • [2] Interview to E. Casas-Alvero in Spanish. https://www.gaussianos.com/la-conjetura-de-casas-alvero-contada-por-eduardo-casas-alvero/.
    • [3] W. Castryck, R. Laterveer, M. Ounaı̈es, Constraints on counterexamples to the Casas-Alvero conjecture and a verification in degree 12,...
    • [4] M. Chellali, On the number of real polynomials of the Casas-Alvero type, J. of Taibah Univ. for Science 9 (2015), 351 – 356.
    • [5] G.M. Dı́az-Toca, L. González-Vega, On analyzing a conjecture about univariate polynomials and their roots by using Maple in “ A Maple...
    • [6] J. Draisma, J.P. de Jong, On the Casas-Alvero conjecture, Eur. Math. Soc. Newsl. 80 (2011), 29 – 33.
    • [7] H.-C. Graf von Bothmer, O. Labs, J. Schicho, C. van de Woestijne, The Casas-Alvero conjecture for infinitely many degrees, J. Algebra...
    • [8] S. Yakubovich, Polynomial problems of the Casas-Alvero type, J. Class. Anal. 4 (2014), 97 – 120.

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