Brändén's Conjectures on the Boros-Moll Polynomials

William Y. C. Chen, Donna Q. J. Dou and Arthur L. B. Yang

  Abstract:  We prove two conjectures of Brändén on the real-rootedness of polynomials Qn(x) and Rn(x) which are related to the Boros-Moll polynomials Pn(x). In fact, we show that both Qn(x) and Rn(x) form Sturm sequences. The first conjecture implies the 2-log-concavity of Pn(x), and the second conjecture implies the 3-log-concavity of Pn(x).

  AMS Classification:  26C10; 05A20, 30C15

  Keywords:  Boros-Moll Polynomials, Real-rootedness, Sturm sequence, 3-log-concavity

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