Jensen polynomials for the Riemann xi-function.

We investigate ξ (s) = 1 2 s (s − 1) π − s 2 Γ (s 2) ζ (s) , where ζ (s) is the Riemann zeta function. The Riemann hypothesis (RH) asserts that if ξ (s) = 0 , then Re (s) = 1 2. Pólya proved that RH is equivalent to the hyperbolicity of the Jensen polynomials J d , n (X) constructed from certain Taylor coefficients of ξ (s). For each d ≥ 1 , recent work proves that J d , n (X) is hyperbolic for sufficiently large n. In this paper, we make this result effective. Moreover, we show how the low-lying zeros of the derivatives ξ (n) (s) influence the hyperbolicity of J d , n (X). [ABSTRACT FROM AUTHOR]