Abstract:  Let d_i(m) denote the coefficients of the Boros-Moll polynomials. Moll's minimum conjecture states that the sequence {i(i+1)(d_i²(m)-d_i-1(m)d_i+1(m))}_{1≤ i≤ m} attains its minimum at with 2^-2mm(m+1). This conjecture is a stronger than the log-concavity conjecture proved by Kausers and Paule. We give a proof of Moll's conjecture by utilizing the spiral property of the sequence {d_i(m)}_{0≤ i≤ m}, and the log-concavity of the sequence {i!d_i(m)}_{0≤ i≤ m}.

  AMS Classification:  05A20; 11B83; 33F99

  Keywords:  ratio monotonicity, log-concavity, Boros-Moll polynomials

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