Branden's Conjectures on the Boros Moll Polynomials
We prove two conjectures of Br\"{a}nd\{e}n on the real rootedness of 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)