Branden's Conjectures on the Boros-Moll Polynomials

作者：Chen William Y C; Dou Donna Q J; Yang Arthur L B^*

来源：International Mathematics Research Notices, 2013, 2013(20): 4819-4828.

DOI：10.1093/imrn/rns193

We prove two conjectures of Branden on the real-rootedness of the polynomials Q(n)(x) and R-n(x) which are related to the Boros-Moll polynomials P-n(x). In fact, we show that both Q(n)(x) and R-n(x) form Sturm sequences. The first conjecture implies the 2-log-concavity of P-n(x), and the second conjecture implies the 3-log-concavity of P-n(x).

• 出版日期2013
• 单位南开大学