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.

• Type: Journal
• Year: 2006
• Where: JAT
• Authors: David A. Cardon, Sharleen A. Roberts
• Keywords: JAT 2006, Orthogonal Polynomials, Riemann Hypothesis, Simple Zeros