An equivalence for the Riemann hypothesis in terms of orthogonal polynomials (Q818456)

The authors construct a measure such that, if \(\{p(z)\}\) is the sequence of orthogonal polynomials relative to that measure, then the Riemann hypothesis with simple zeros is true if and only if \[ \lim_{n\to\infty}\,{p_{2n}(z)\over p_{2n}(0)}= {\xi(1/2+ iz)\over\xi(1/2)},\quad\text{where}\quad \xi(s)= {1\over 2} s(s- 1)\pi^{-s/2}\Gamma(s/2)\,\xi(s) \] is the Riemann \(\xi\)-function.