An equivalence for the Riemann Hypothesis in terms of orthogonal polynomials

We construct a measure such that if {pn(z)} is the sequence of orthogonal polynomials relative to that measure, then the Riemann Hypothesis with simple zeros is true if and only if limn→∞ p2n(z) p2n(0) = (1/2+iz) (1/2) where (s)= 1 2 s(s − 1) −s/2 (s/2) (s) is the Riemann -function. © 2005 Elsevier Inc. All rights reserved.