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_i ²(m)-d_i-1(m) d_i+1(m))}_{1≤ i≤ m} attains its minimum at i = m with 2^-2mm(m+1) . This conjecture is a stronger than the log-concavity conjecture of Moll proved by Kauers 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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